If (a+b):(a-b) = 1:5, then (a^2 - b^2):(a^2 + b^2) equals

Anup Sahay   9 years AGO

given a+b/a-b=1/5
so apply componendo and dividendo method here
so (a+b+a-b)/(a+b-a+b)=1+5/1-5
so a/b=6/-4
put a=6 and b=-4 in (a^2-b^2):(a^2+b^2)
which on calculations comes to be 20:52
i.e. option 5) 5:13

Like? Yes (15) | No (3)  

Ajeet Kumar   9 years AGO

let a=3, b=-2
then a^2-b^2/a^2+b^2=5/13

Like? Yes (12) | No (2)  

Sruthi Sreejan   9 years AGO

(a+b):(a-b) = 1:5
=>a/b= -3/2
so
(a^2 - b^2):(a^2 + b^2)
dividing numerator and denomenator with b^2,we get
(a/b)^2 - 1 : (a/b)^2 +1
substituting value for a/b, we get
5/13

Like? Yes (8) | No (2)  

praveendas   9 years AGO

by solving given equations we get a=3,b=-2.
ans is 5:13

Like? Yes (4) | No   

kriti kankariya   9 years AGO

applying componendo dividendo
a/b = -3/2
i.e. a=-3b/2
putting in required eq.
((-3b/2)^2 - b^2 ) / ((-3b/2)^2 + b^2 )
= 5/13

Like? Yes (4) | No   

anvitha   9 years AGO

By Solving two eqns a+b=1 & a-b=5 we get a=3 &b= -2
by substituting in the gvn qtn we get 5:13

Like? Yes (4) | No (1)  

shivam dubey   9 years AGO

A+b = 1
A-b = 5


A = 3
B = -2

So
(9-4)/(9+4)

5/13

Like? Yes (3) | No   

Sivaprakash.J   9 years AGO

a+b:a-b=1:5
a+b/a-b=1/5
From this,
a=-6b/4
So (a^2-b^2):(a^2+b^2)
Can be written as (a^2-b^2)/(a^2+b^2)=((-6b/4)^2-b^2)/((-6b/4)^2+b^2)
=20b^2/52b^2
=5/13
So the answer is 5:13

Like? Yes (3) | No   

meghana   9 years AGO

(a+b):(a-b)=1:5

[1+(b:a)]:[1-(b:a)] =1:5

[1+(b:a)]*5 = [1-(b:a)]

b:a= (-2:3)

(b:a)^2 = 4:9

(a^2-b^2):(a^2+b^2) = [1-(b:a)^2]:[1+(b:a)^2]


= [1-(4:9)]:[1+(4:9)]

= 5:13

Like? Yes (3) | No   

SAGNIK DATTA   9 years AGO

5(a+b)=a-b
a=(6/4)b
now let b=4 so a=6
now solving ans=5:13

Like? Yes (6) | No (4)  

Aniket choudhary   9 years AGO

on solving a=-3/2*b,after that putting the value in original equation we will get the value i.e option 5

Like? Yes (2) | No   

bharath   9 years AGO

a+b=1
a-b=5
then a=3, b=-2
then a^2-b^2:a^2+B^2=5:13

Like? Yes (2) | No   

umang agarwal   9 years AGO

5(a+b)=a-b;
=>a=-3/2*b;
(9/4*b^2-b^2)/(9/4*b^2+b2)=5/13 ans...

Like? Yes (2) | No   

santosh kumar patel   9 years AGO

(a+b):(a-b)=1:5
so a+b/a-b=1/5
after solving, we get
a/b=-3/2
hence a= -3 and b= 2
so solve the next condition i found
5:13

Like? Yes (2) | No   

Chitra.S   9 years AGO

a+b:a-b=1:5
5a+5b=a-b
2a=-3b
a:b=-3:2.
Therefore,a2-b2/a2+b2=5:13

Like? Yes (3) | No (1)  

shameer guptha   9 years AGO

just take a+b=1 and a-b=5
by solving we get a=3,b=-2
so ans is 5:13 by solving

Like? Yes (2) | No   

sireesha.yammanuru   9 years AGO

a/b = (-3)/2
a^2/b^2 = 9/4
by componendo & dividendo it will be 5:13

Like? Yes (2) | No   

shibanti sanyal   9 years AGO

Solving, 5a+5b=a-b.

Therefore, a=(-3/2)b

Putting this value in given ratio, answer obtained is 5:13.

Like? Yes (2) | No   

Koushik Modak   9 years AGO

a:b= -3/2
so a^2/b^2=9/4
then a^2-b^2/a^2-b^2= 5/13

Like? Yes (2) | No   

SUMAN KUMAR   9 years AGO

(a+b)(a+b)/(a-b)(a+b)=1/5
((a^2+b^2)/(a^2-b^2))-+(2ab/(a^2-b^2))=1/5
(a^2-b^2)/(a^2+b^2)=5/13

Like? Yes (2) | No   

Asha Verma   9 years AGO

From given a =-(3/2)b
On putting we get 5/13

Like? Yes (2) | No   

DHAYYALA SREEKANTH REDDY   9 years AGO

5(a+b)=a-b
by solving this we got a=(-6/4)b
substitute this in a^2-b^2/a^2+b^2
then we this ratio as 5:13

Like? Yes (2) | No   

H. Sreekanth   9 years AGO

If we solve we get a=-6b/4;
substitute a in (a^2 - b^2):(a^2 + b^2) we get 5:13

Like? Yes (2) | No   

pavan   9 years AGO

by solving a:b=-3;2 then ((a/b)^2-1):((a/b)^2+1)=9-4:9+4=5;13

Like? Yes (2) | No   

kiran   9 years AGO

a^2-b^2=(a+b)(a-b)
a^2+b^2=(a+b)^2-[(a+b)^2-(a-b)^2]/2
substituting a+b=1 and a-b=5 we get 5:13

Like? Yes (2) | No   

ADUSUMALLI VAMSI KRISHNA   9 years AGO

a+b = 1 and a-b = 5 then a= 3 , b=-2 so a^2-b^2 : a^2+b^2= 5:13

Like? Yes (2) | No   

Anubrindha   9 years AGO

(a^2-b^2)= (a-b)(a+b)
(a^2+b^2)=(a^2+b^2)-2ab

(a-b)(a+b)/((a^2+b^2)-2ab) =(1*5)/(1-2ab)

By solving (a^2+b^2)/(a^2-b^2)=1/5
a/b= (-3/2) Therefore a= -3 and b= 2
5/(1-2ab)= (5/1+12)
5/13 = 5 :13

Like? Yes (2) | No   

REVATHIVENKATESAN   9 years AGO

a+b/a-b=1/5;
so a+b=1 and a-b=5;
(a^2-b^2)/(a^2+b^2)=2*(a^2-b^2)/(a^2+b^2)*2;
=(2*(a+b)*(a-b))/((a+b)^2+(a-b)^2)
=(2*1*5)/(1^2)+5^2
=10/26
=5/13
so answer is 5:13

Like? Yes (2) | No   

kalyan ram   9 years AGO

a^2+b^2=((a+b)^2+(a-b)^2)/2 & a^2-b^2=(a+b)(a-b)
now ((a+b)(a-b))/((a+b)^2+(a-b)^2)/2=2/(1/5)+5=5/13

Like? Yes (2) | No   

shilpa hs   9 years AGO

if we take a=3,b=-2 we will get (a+b):(a-b)=1:5
and (a^2-b^2):(a^2+b^2)=5:13

Like? Yes (2) | No   

VADLA CHANDRA SHEKHAR   9 years AGO

a^2-b^2=(a+b)x(a-b)=1*5=5
(a+b)^2+(a-b)^2=2(a^2+b^2)=26
(a^2+b^2)=13
resultant=5/13

Like? Yes (2) | No   

lavanya   9 years AGO

a^2-b^2=(a+b)*(a-b)
so 5*1=5
a^2+b^2=(a+b)^2-(a-b)^2
so 1^2+5^2=26
then answer is 5:26

Like? Yes (2) | No   

Gunavathy.R   9 years AGO

a^2-b^2=(a+b)(a-b);
a+b=1,a-b =5;
so 1*5=5;

Like? Yes (2) | No   

Danda Sindhura   9 years AGO

Let a+b=1x
a-b=5x
On solving we get a=3x
b=-2x
by substituting these values in a^2-b^2:a^2+b^2 we get 5:13

Like? Yes (2) | No   

vishal varma   9 years AGO

(a+b)/(a-b) =1/5
5a+5b=a-b
2a=-3b
(9/4*b^2-b^2)/(9/4*b^2+b^2) =5:13

Like? Yes (2) | No   

velmala gangadhar   9 years AGO

a^2+b^2=1/2[(a+b)^2+(a-b)^2]
from given equn...(a-b)^2=25(a+b)^2...
5(a+b)^2:1/2[(a+b)^2+(a-b)^2]...
...5:13...

Like? Yes (2) | No   

p.supriya   9 years AGO

by sustituting the value of a =-3/2b
in the equation we get 5:13

Like? Yes (2) | No   

Sowjanya Surisetty   9 years AGO

clearly given that (a+b):(a-b)=1:5
then by cross multiplication& equating we get 2a+3b=0
them b=-2a/3
substitute this in given question
then we get (a^2-(4a^2/9))/(a^2+(4a^2/9))
now we get the answer as 5:13

Like? Yes (2) | No   

MADDALI HEMA NARAYANA   9 years AGO

from the given relation we can get relation between a and b as a=(-3/2)b
just we have to substitute this value in the asked question then we can get 5:13

Like? Yes (2) | No   

Lakhi kant Roy   9 years AGO

(a+b)/(a-b)=1/5, by solving we get,
a=(-3b/2)^2, put this value in (a^2-b^2)/(a^2+b^2),
we get,
{(-3b/2)^2-b^2} / {(-3b/2)^2+b^2},
by solving this we will get, 5/13
so required ratio=5:13

Like? Yes (2) | No   

Ayush Singhal   9 years AGO

(a+b)/(a-b)=1/5
5a+5b=a-b
2a=-3b
a/b=-3/2
(a^2-b^2)/(a^2+b^2)=((a^2/b^2)-1)/((a^2/b^2)+1)
put the value of a/b & then calculate
ans is 5/13

Like? Yes (2) | No   

AARTI OJHA   9 years AGO

a/b=-3/2
thus, a^2/b^2=9/4
further,a^2-b^2/a^2+b^2=5/13

Like? Yes (2) | No   

Sakshi Agarwal   9 years AGO

A+B/A-B=1/5
By components dividendo.
A/b=3/(-2)
A^2 / B^2 =. 9/4
Applying componendo dividendo..
A^2+b^2/ a^2-B^2 = 13/5

Ans. 5/13

Like? Yes (2) | No   

Pallavi Reddy   9 years AGO

formulae for a^2-b^2 is (a+b)(a-b) and the formulae for
a^2+b^2 is (a+b)^2+(a-b)^2/2
we have values for both (a+b) and (a-b)
so we can solve it easily

Like? Yes (2) | No   

pavandeep singh ubbi   9 years AGO

by taking a common in both tha eq.... and finding the value of b/a and putting it on other eq

Like? Yes (2) | No   

AMIT KUMAR   9 years AGO

(a+b) /(a-b) =1/5
So,a/b=-3/2
(a2-b2)/(a2+b2)={(a2/b2)-1}/{(a2/b2)+1}
={(9/4)-1}/{(9/4)+1}
=5/13

Like? Yes (2) | No   

shivom pandey   9 years AGO

get value of (a/b) from equation 1 & then get the a/b =(-3/2) .



put in second equ and get 5/13

Like? Yes (2) | No   

Udita Maitra   9 years AGO

a+b/a-b=1:5
by componendo dividendo,
a/b=-3/2
a^2/b^2=9/4
(a^2-b^2):(a^2+b^2)=5:13

Like? Yes (2) | No   

MATLOOB HUSAIN   9 years AGO

2a=-3b
and then value a put in second expression and get 5:13,

Like? Yes (2) | No   

aman aditya   9 years AGO

a=3
b=-2
so
5:13

Like? Yes (3) | No (2)  

ajay kulkarni   9 years AGO

from 1st equation we get value of a=(-3/2).
put this value in second equation we get
ans=5/13

Like? Yes (1) | No   

sudiptaa   9 years AGO

(a+b)/(a-b)=1/5
a=-3/2b
(a^2 - b^2)/(a^2 + b^2)= 5/13

Like? Yes (1) | No   

Kunal nemu   9 years AGO

Let (a - b)=5k,,and (a + b)=k
So we get a=3k,and b= -2k
ab= -6 k^2
(a^2-b^2)=(a-b)*(a+b) =5k * k =5 k^2
(a^2+b^2)=(a+b)^2 -2*a*b=k^2 - 2*3k* -2k=k^2+12k^2=13k^2
therefore (a^2 - b^2) : (a^2+b^2)=5:13

Like? Yes (1) | No   

Deepak kumar kumawat   9 years AGO

5a-5b=a+b
a/b=3/2
a^2/b^2=9/4
(a^2-b^2)/(a^2+b^2)=5/13
hence option 5

Like? Yes (1) | No   

vikas kulshrestha   9 years AGO

a+b/a-b= 1
by componendo and dividendo method,
a/b=-3/2
a=-3b/2
a^2-b^2/a^2+b^2= 5/13

Like? Yes (1) | No   

Monika Nemiwal   9 years AGO

(a+b):(a-b)=1:5,means
(a+b)=x
(a_b)=5x
on solving, we get :a=3x
b=-2x
thus,(a^2-b^2):(a^2+b^2)=(9-4)x^2:(9+4)x^2
=5:13

Like? Yes (1) | No   

ishan chourishi   9 years AGO

a=3 and b=(-2) is satisfying the first condition.
putting values on right side we get ratios 5:13

Like? Yes (1) | No   

Akash Kumar   9 years AGO

(a+b)/(a-b)=1/5 is given
by Componendo and dividendo rule
{if a/b=c/d then (a+b)/(a-b)=(c+d)/(c-d)}
a/b=-(3/2)
(a^2-b^2)/(a^2+b^2)
=[(a/b)^2-1]/[(a/b)^2+1]
=[(9/4)-1]/[(9/4)+1]
=(5/4)/(13/4)
=5/13 => 5:13
Therefore option 5 is true.

Like? Yes (1) | No   

ramya   9 years AGO

From the given question: we get a=3 and b= -2
So the answer is 5:13 for (a^2-b^2):(a^2+b^2)

Like? Yes (1) | No   

RAVAL   9 years AGO

a+b+a-b : a+b-a+b = 6 : -4
so,
a : b = 3 : -2
a^2+b^2 : a^2-b^2 = (9-4) : (9+4)
= 5 : 13

Like? Yes (1) | No   

Pronab Paul   9 years AGO

a+b/a-b=1/5
a=-3b/2
((-3b/2)^2-b^2)/((-3b/2)^2+b^2)=5b^2/13b^2=5:13

Like? Yes (1) | No   

rashmi r m   9 years AGO

Select a=6,b=-4. So that it satisfy the given equation..
Then appling a and b values to (a^2-b^2):(a^2+b^2)=5÷13

Like? Yes (1) | No   

Shubham Raj   9 years AGO

from question-
(a+b) / (a-b) = 1/5
so, 5a+5b = a-b
=> 4a+6b =0
=> 2a = -3b
=> a = (-3b) / 2
now, (a+b)(a-b) / (a+b)^2 -2ab
=>( ( -3b/2 +b)(-3b/2 -b) ) / (((-3b + b)/2)^2 - 2* -3b/2 *b)
=> (5b^2/4 ) / (13b^2 / 4)
=>5 : 13
therfore
(a^2 - b^2):(a^2 + b^2) equals 5:13

Like? Yes (1) | No   

md shabbir ahmad   9 years AGO

from given cond ,
a+b/a-b=1/5
b(a/b+1)/b(a/b -1)=1/5
then a/b=-3/2
we can write a^2-b^2/a^2+b^2 as
b^2[a^2/b^2-1]/b^2[a^2/b^2+1]
then we can put the value of a/b
then we get
5/13

Like? Yes (1) | No   

vivek   9 years AGO

By solving eq we get a=3 and b=-2,
So , required result is 5:13

Like? Yes (1) | No   

vinod   9 years AGO

a is 3 and b is -2...so a+b is 1 and a-b will be 5


same way square of a is 9 and square of b is 4...substitute in the required and u l get the answer as 9-4:9+4=5:13

Like? Yes (1) | No   

chindam laxman   9 years AGO

(a^2-b^2)/(a^2+b^2)=(a+b)(a-b)/0.5[(a+b)^2+(a-b)^2]
if we simlify
we know a+b=(a-b)/5
so we get finaaly
5/13 is our Ans. i.we 5:13

Like? Yes (2) | No (1)  

VISHAL.MORI   9 years AGO

There are two equations are given, By solving this we gate A=3 & B=-2.
now sqare and get ans.5:13

Like? Yes (1) | No   

PIYUSH AGRAWAL   9 years AGO

there are two variable A and b so by supposing value of a=3
b=-2 and butting this value we find this solution

Like? Yes (1) | No   

SHOWMIA DAISY RAJENDRAN   9 years AGO

a^2- b^2= (a+b)(a-b)
a^2+b^2= 1/2{[(a+b)^2]+[(a-b)^2]}
by calculating the values as given,
a+b=1 and a-b=5
we will be getting the final value as 5/13.

Like? Yes (1) | No   

Vishu   9 years AGO

(a+b)/(a-b) = 1/5
a = -(3/2)b
Put in second u will get the ratio as 5:13

Like? Yes (1) | No   

tamilmani   9 years AGO

assume a=3
b=-2
a+b=1
a-b=5
a^2-b^2=9-4=5
a^2+b^2=9+4=13
ans: option 5
(5:13)

Like? Yes (1) | No   

siddhi datri   9 years AGO

as a+b/a-b=1/5
=>a/b=-3/2
=>a=-3b/2
therefore, (a^2 - b^2):(a^2 + b^2)=(9/4-1)/(9/4+1)=5/13

Like? Yes (1) | No   

Suraj   9 years AGO

5a+5b=a-b
4a+6b=0
a/b=-6/4
ans=5/13

Like? Yes (1) | No   

Belal Ahmed   9 years AGO

by usual method we get a=-3b/2
by substitution we get ans as 5:13

Like? Yes (1) | No   

Rituparna Chakraborty   9 years AGO

(a+b)/(a-b)=1/5=>a=-3b/2
Now (a^2-b^2)/(a^2+b^2)
putting the value that a=-3b/2
we get the value of given expression 5/13.
so required ratio=5:13

Like? Yes (1) | No   

Dwaipayan Goswami   9 years AGO

by solving first equation we get a =-3/2b. Now in second equation replace each a by -3/2b. You'll get 5/13

Like? Yes (1) | No   

Santhosh R   9 years AGO

then
(a^2-b^2)/(a^2+b^2)
=(2(a+b)(a-b))/((a-b)^2+(a+b)^2)
=(2*(1/5)*(a-b)^2)/((a-b)^2+(1/25)(a-b)^2)
=(2/5)*(25/26)
=5/13=Ans

Like? Yes (1) | No   

nitin rawat   9 years AGO

(a/b+1)/(a/b-1)=1/5;
so a/b=-3/2;
Putting value of a/b in 2nd eqn.
((a/b)^2-1)/((a/b)^2+1)=5/13

Like? Yes (1) | No   

Ajay Kumar Gupta   9 years AGO

from given ratio we found => b=(-2/3)*a
so (a^2-b^2)/(a^2+b^2)=(5/9)a^2/(13/9)a^2
so ratio is 5:13.

Like? Yes (1) | No   

Arpan Datta   9 years AGO

a+b/a-b = 1/5
so, a= -3b/2
puttin the valu of a,
the ans is 5/13

Like? Yes (1) | No   

pratik avinash   9 years AGO

a+b= 1 ----- eq. 1
a-b= 5 -----eq. 2
solving both we will get
a= 3, b= -1
so,
(a^2 - b^2):(a^2 + b^2) = 5/13

Like? Yes (1) | No   

gidda reddy   9 years AGO

Suppose a=3,b=-2
Substitute in
(a+b) :(a-b) =1:5
So Substitute in a& b values
(a^2-b^2) :(a^2+b^2) =5:13

Like? Yes (1) | No   

Lakhan H. Jadhav   9 years AGO

a+b=1,
a-b=5
After solving a=3, b=-2,
so put this values in given equation

Like? Yes (1) | No   

Ankit   9 years AGO

(a+b)/(a-b)=1/5, Applying componendo and dividendo, we get a/b=-(3/2). therefore answer will be 5:13

Like? Yes (1) | No   

tarun kumar rajak   9 years AGO

5(a+b)=a-b
=> a= -3b/2

put value in eq

Like? Yes (1) | No   

Deepanshu Chaturvedi   9 years AGO

(a+b)/(a-b)=1/5
so, a= (-3/2)b
(a^2 - b^2):(a^2 + b^2)=5/13

Like? Yes (1) | No   

Sanjeev Tiwari   9 years AGO

use componendo and dividendo for the first ratio. which will give a/b=3/-2. Substitute in 2nd ratio to get the answer.

Like? Yes (1) | No   

Nilesh Dattatraya Veer   9 years AGO

a+b=1
a-b=5
solve these equation
we get a=3 b=-2
put thivalues

Like? Yes (1) | No   

neha gupta   9 years AGO

(a+b):(a-b) = 1:5
Using componendo and dividendo in above equation, we get
a:b = -3:2
squaring both sides:
a^2 : b^2 = 9:4
againg using componendo and dividendo
(a^2 + b^2):(a^2 - b^2) = 13:5
thus (a^2 - b^2):(a^2 + b^2) = 5:13

Like? Yes (1) | No   

Manikanta   9 years AGO

let a+b=x
a-b=5x
by solving the Above equations a=3x; b=2x
then a^2-b^2=5x^2
a^2+b^2=13x^2
so the ratio=5/13

Like? Yes (1) | No   

IMRAN UL HAQUE   9 years AGO

a+b/a-b=1/5
using coponando and dividando formulaa and putting value we get
a=3/2b
put this value in requier equatio
we get
answer 5:13

Like? Yes (1) | No   

Abhishek Anand   9 years AGO

a+b = 1 .......................eqn 1
a -b = 5 .......................eqn 2
Adding the above two eqn,we got
a=3 and b= -2
Now,Calculating (a^2-b^2)/(a^2+b^2) we get 5/13 Ans.

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Gousulu K   9 years AGO

a+b/a-b=1/5
a+b=1
a-b=5
solving we get
a=3,b=-2
(a^2-b^2)/(a^2+b^2)=5/13

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Surendra Naraga   9 years AGO

a+b=1
a-b=5
so a=3 and b=-2
a^2-b^2/a^2+b^2=
5/13
5:13

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venkatesh   9 years AGO

Here,
a+b=5,
a-b=1;
then, a=3,b=-2...
Hence (a^2 - b^2):(a^2 + b^2)=5:13.

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YASWANTH REDDY   9 years AGO

(a+b):(a-b) = 1:5
by componendo and dividendo, we get a=3 and b=-2
therefore (a^2 - b^2) : (a^2 + b^2) = 5:13

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UDIT   9 years AGO

(a+b)/(a-b)=1/5
solving we get a=(-3b/2)
putting value of 'a' in (a^2-b^2)/a^2+b^2)
solving we get ratio=5:13(option 5)

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Sandip Shaw   9 years AGO

(a+b)/(a-b)=1/5
a/b=(-3/2)
a^2/b^2=9/4
(a^2-b^2)/(a^2+b^2)=(9-4)/(9+4)=5/13

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M.V.S sai sunidhi   9 years AGO

(a+b)/(a-b)=1/5,from this either calculate a or b value
5(a+b)=a-b
5a-a=-b-5b
a=-(3b/2)
keep this a value in the equation(a^2-b^2)/(a^2+b^2)
((-3b/2)^2-b^2)/((-3b/2)^2+b^2)=5/13

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Wenveil lius   9 years AGO

A+b=¹
A-b=5
On solving a=3,b=-2

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shiva   9 years AGO

ans:5 option
(a+b)/(a-b)=1/5
then 5a+5b=a-b
a/b=-3/2 so a=-3 and b=2 then ans is 5:13

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Sarika A S   9 years AGO

a+b=1/6,a-b=5/6
a^2-b^2=(a+b)(a-b)
a^2+b^2=[(a+b)^2-(a-b)^2]/2
so ans is 5/13

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Sushmita Ghanty   9 years AGO

a+b/a-b=1:5
a/b=-3/2
so, (a^2-b^2)/(a^2+b^2)=5/13

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rituraj   9 years AGO

i solved it

(2*(a+b)(a-b))/(a+b)^2+(a-b)^2

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