The sum of reciprocal of two numbers is 0.45 and the sum of reciprocal of their squares is 0.1025, t

Akanksha Mishra   11 years AGO

Suppose Two numbers are x and y and its reciprocals
are 1/x and 1/y
According to the question

1/x + 1/y = 0.45------(1)

1/x^2 + 1/y^2 = 0.1025-----(2)

According to 1st equation
1/4 + 1/5 = 0.45

According to 2nd equation
1/4^2 + 1/5^2 = 0.1025
So x = 4
y = 5

I hope my solution will easy to understand

Like? Yes (29) | No (16)  

Udhaya kumar   11 years AGO

(1/x) + (1/y) = 0.45 .....a
(1/x)^2 + (1/y)^2 = 0.1025 ......b
From a we get 1/y = 0.45 - (1/x)
sub this in b we get
(1/x)^2 + (0.45 - (1/x))^2 = 0.1025
by solving we get
2(1/x)^2 - (0.9/x) + 0.1 = 0
by solving this eqn we get
1/x = 0.25 , 0.2
we want x so
x = 1/0.25 , 1/0.2
x = 4 , 5.................

Like? Yes (12) | No (6)  

Pradyumna K S   11 years AGO

(1/4)+(1/5)=0.45
(1/16)+(1/25)=.1025

Like? Yes (3) | No (1)  

sujata   11 years AGO

1/4 = 0.25 and 1/5 = 0.2
=0.25+0.20 = 0.45

1/16= 0.0625 and 1/25 = 0.04
=0.0625+0.04 = 0.1025

Like? Yes (2) | No (1)  

R.RAVIKUMAR   11 years AGO

1/x+1/y=0.45 i.e. (x+y)/xy=0.45
and (1/x^2+1/y^2)=0.1025
from (1/x+1/y)^2=1/x^2+1/y^2+2/xy
so, 0.2025=0.1025+0.9/(x+y)
it gives x+y=9
by solving first equation it gives xy=20
so, the answer is 4 and 5...

Like? Yes (2) | No (1)  

Rajasekhar Reddy   11 years AGO

given that
1/x + 1/y = 0.45
1/x^2 + 1/y^2 = 0.1025

(1/x + 1/y)^2 = 0.45^2
from this we get
x+y = 9
now we can verify the options easily

Like? Yes (2) | No (1)  

D.Mamatha   11 years AGO

A/c to given data....

let numbers be X ,Y

(1/X)+(1+Y)= 0.45

(1/X)^2+(1/Y)^2= 0.1025

By using (a+b)^2 formula

(1/X)^2 + (1/Y)^2 = (1/X + 1/Y)^2 - 2(1/X)(1/Y)

0.1025 = (0.45)^2 - 2/(XY)

XY = 20

So, The numbers are 4,5

Option is 2.

Like? Yes (2) | No (1)  

sandy   11 years AGO

1/4+1/5=0.45
1/4^2+1/5^2=0.1025

Like? Yes (2) | No (1)  

LOGAN WOLVERINE   11 years AGO

option 2.
1/4+1/5=0.45

Like? Yes (1) | No   

AMIT JAISWAL   11 years AGO

according to question two equation will be formed
1/x+1/y=0.45
1/x^2+1/y^2=0.1025

and on putting 4 & 5 in place of x and y the equation will be satisfied.

Like? Yes (1) | No   

Anantharaman   11 years AGO

1/4 + 1/5 = 0.45

1/16 + 1/25 = 0.1025

so numbers are 4, 5

Option 2

Like? Yes (1) | No   

amit bhagat   11 years AGO

according to question two equation will be formed
1/x+1/y=0.45
1/x^2+1/y^2=0.1025

and on putting 4 & 5 in place of x and y the equation will be satisfied.

Like? Yes (1) | No   

yarasi meena   11 years AGO

1/4=0.25 and 1/5=0.2
sum of these two is 0.45
1/16=0.0625 and 1/25=0.04 . sum of these two is 0.1025
so the numbers are 4,5

Like? Yes (1) | No   

K.ARun   11 years AGO

1/4 + 1/5 = 0.45
(1/4)^2+(1/5)^2=0.1025

Like? Yes (1) | No   

Leelanand Kumar Yalla   11 years AGO

Let us take two numbers x,y......
Reciprocal of two numbers sum is (x+y)/xy=0.45;
(x+y)= 0.45xy;
sum of Reciprocal of their squares is 0.1025;
(x^2+y^2)/x^2*y^2=0.1025;
(x^2+y^2)= 0.1025x^2*y^2;
By solving these two we will get 4,5.....

Like? Yes (1) | No   

Gurmeet Singh   11 years AGO

1/X + 1/y= 0.45

1/x^2 + 1/y^2 =0.1025

Solving this
X=4 and y=5

Like? Yes (1) | No   

T.Aravinth kumar   11 years AGO

given:
1/x+1/y=0.45
take above equation and substitute our choice
1/4+1/5=0.45.

Like? Yes (3) | No (2)  

Arigela Naga Vineel   11 years AGO

by referring options we can solve 4,5 are numbers

Like? Yes (1) | No   

rajdeep pal   11 years AGO

let two no be x and y
1/x+1/y=.45
1/x^2+1/y^2=.1025 (1+x+1/y)^2-2/xy=.1025
therefore solvng fr x,y
ans..4,5

Like? Yes (1) | No   

KRISHNAN   11 years AGO

let the number be x and y
so 1/x +1/y = 9/20

and 1/x2 + 1/y2 = 10.25/100

Solving the equation we get x = 4 and y = 5

Like? Yes (1) | No   

Aditya Verma   11 years AGO

let two numbers are x and y
now sum of their reciprocal => 1/x+1/y= 0.45
and sum of reciprocal of their square=> 1/x^2+1/y^2=0.1025
now cross check than 4 and 5 numbers are satisfied equation first then answer is option 2
4 and 5

Like? Yes (1) | No   

paulprashanth   11 years AGO

(1/4)+(1/5)=o.45
(1/16)+(1/25)=0.1025

Like? Yes (1) | No   

SONU GUPTA   11 years AGO

sum of two recipocal number
1/x+ 1/y=0.45
so given option
1/4+ 1/5= 9/20=0.45
and their squre
1/16+ 1/25=41/400=0.1025

Like? Yes (1) | No   

krishna   11 years AGO

sum of 2 reciprocal of two no. = 0.45
(1/x)+(1/y) = 0.45 ----- (1)
then the sum of reciprocal of their squares is = 0.1025
(1/x)^2 + (1/y)^2 = 0.1025 ------ (2)
let take 1/x = a and 1/y =b for our convinced
so
eq(1)==> a+b = 0.45
eq(2) ==> a^2 + b^2 = 0.1025
(a+b)^2 = a^2+b^2 +2ab
0.2025 = 0.1025 + 2ab
2ab = 0.1
ab= 0.05
now (a-b)^2 = (a+b)^2 - 4ab
= 0.2025 - 4(0.05)
= 0.0025
a-b = 0.05
a+b=0.45
a-b=0.05
from above equations we get a=0.25 and b =0.2
so a= 1/x =0.25 ==> x= 4
b=1/y = 0.2 ===> y=5
so two numbers are x=4,y=5

Like? Yes (1) | No   

Sneha   11 years AGO

Let the 2 numbers be x and y.
Given,(1/x)+(1/y)=0.45 & (1/x^2)+(1/y^2)=0.1025
By squaring on both sides for 1st eq and solving
then x=4 and y=5

Like? Yes (1) | No   

manikanta   11 years AGO

by checking options ..... 1/x+1/y=0.45 put x=4 y=5 ie option 2 satisfy that equ like that we can also find out (1/x)2++(1/y)2......

Like? Yes (1) | No   

Sukanya   11 years AGO

The answer is 4,5.
sum of the reciprocals is 1/4+1/5=0.45.
sum of reciprocals of their square is 1/16+1/25=0.1025

Like? Yes (1) | No   

Mayuri Rangari   11 years AGO

let d 2 no r: x & y
from given
1/x+1/y=0.45 =>x+y=0.45xy =>(x+y)^2=0.2025*x^2*y^2.....(1)
nw 2nd eq.
(1/(x^2))+(1/(y^2))=0.1025 =>x^2+y^2=0.1025......(2)
from eq. (1) & (2)
x*y=20
hence ans 4, 5

Like? Yes (1) | No   

Naveen Pandey   11 years AGO

1/a+1/b=0.45
1/a2+1/b2=0.1025..
solving we get a,b=4,5

Like? Yes (1) | No   

Anup Kumar Sharma   11 years AGO

1/a + 1/b=0.45 and 1/a^2 + 1/b^2=0.1025

so squaring first equation is 1/a^2 + 1/b^2 + 2/ab=0.2025
now subtract second equation from this to get ab=20
and product of only 4 and 5 is 20

Like? Yes (1) | No   

piyush   11 years AGO

let x and y be two numbers
1/x + 1/y = 0.45
reducin 0.45 answer is 9/20
therefore lcm of two number shud be 20 and their sum should be 9. Only 4 and 5 satisfies this.
And option 2 satisfies this.

Like? Yes (1) | No   

Dinesh thatti   11 years AGO

from options we go we get answer take 2nd option

The sum of reciprocal of two numbers
1/4+1/5=0.45

the sum of reciprocal of their squares
1/16+1/25=0.1025

Like? Yes (1) | No   

mirtunjay verma   11 years AGO

because (1/4)+(1/5)= 0.45
and (1/16) + (1/25) = 0.1025

Like? Yes (1) | No   

teja srinivas   11 years AGO

By verification 1/4=0.25 and 1/5=0.2=>0.2+0.25=0.45
similarly 1/16=0.0625,1/25=0.04=>>0.04+0.0625=0.1025

Like? Yes (1) | No   

Bandi Myna   11 years AGO

by using (a+b)^2 formula we can get ab=20 by option verification we can get the answer

Like? Yes (1) | No   

Bharat Bhushan Jha   11 years AGO

let 1 st no =x
2 nd no=y
then 1/x+1/y=45/100=9/20
only option 2 satisfy

Like? Yes (1) | No (1)  

rupireddy bharath kumar   11 years AGO

let 2 numbers be x and y
given that
step 1:(1/x)+(1/y)=45/100;
step 2:(1/x^2)+(1/y^2)=1025/10000;
square on both side of step 1 we get
(1/x^2)+(1/y^2)+(2/xy)=2025/1000;
substitute step 2 we get (2/xy)=1/10;
from step 1 and 1/xy=1/20;
we get x=4,y=5 or x=5,y=4;

Like? Yes (2) | No (2)  

Devendra Marghade   11 years AGO

If two numbers are a & b
Given,(1/a)+(1/b)=0.45, a+b/(ab)=0.45 or
a+b=0.45ab --(i)
Also (1/a^2)+(1/b^2)=0.1025, or
a^2+b^2=0.1025(a^2)(b^2) --(ii)
From (i),(a+b)^2=(0.45ab)^2
a^2+b^2+2ab=0.2025(a^2)(b^2)
Substituting value of a^2+b^2 from (ii)
0.1025(a^2)(b^2)+2ab=0.2025(a^2)(b^2)
ab=20
Solution can be either (2,10) or (4,5)
(a,b)=(4,5) satisfies the above condition.

Like? Yes (1) | No (1)  

Prabhat Yadav   11 years AGO

by hit and trial

Like? Yes (1) | No (1)  

A.Sivapriya   11 years AGO

Let us assume two numbers x and y

According to the given condition

(1/x)+(1/y) = 0.45

(1/x)^2 + (1/y)^2 = 0.1025

Apply (a+b)^2 formula

(1/x + 1/y)^2 = (1/x)^2 + (1/y)^2 + 2(1/x)(1/y)

(0.45)^2 = 0.1025 + 2/(x.y)

x.y = 20

So, the Numbers are 4,5.

Option is 2.

Like? Yes (2) | No (2)  

YUVAN SATHAIAH   11 years AGO

Let
taken two numbers is 4 & 5.
the sum of reciprocal of two numbers is
=1/4+1/5
=(5+4)/20
=9/20
=0.45

the sum of reciprocal of their squares is
=1/16+1/25
=(25+16)/400
=41/400
=0.1025
so option 2) 4, 5

Like? Yes (1) | No (1)  

P Niranjan   11 years AGO

let the reciprocal numbers are x,y
So,
x+y = 0.45---------------(1)
square on both sides
x^2+y^2+2*x*y = 0.45------(2)
x^2+y^2 = 0.1025---------(3)
substracting (3) from (2)
2xy = 0.1
xy = 0.05

1/xy = 20

so the product of two numbers should equal to 20
this condition holds for 5 and 4 only from the given options

Like? Yes (1) | No (1)  

Satyendra Singh   11 years AGO

1/x + 1/y = 0.45 .....(1)
1/x^2 + 1/y^2 = 0.1025 .....(2)
step 1 do square of equation (1)
1/x^2 + 1/y^2 + 2/xy = 0.2025 ...(3)
replace 1/x^2 +1/y^2 value in ..(2)
=> 2/xy = 0.2025-0.1025
=> xy = 20...(4)
=> from eq..(1) y + x/xy = 0.45
=> y + x = 9...(5)
=> y + 20/y = 9
=> y^2 -9y + 20 = 0
=> y = 5,4
=> x = 4
=>

Like? Yes (1) | No (1)  

pranitha karnati   11 years AGO

let two numbers be a,b
from given, (1/a)+(1/b)=0.45---> eqn (1)
and (1/(a*a))+(1/(b*b) )= 0.1025-->eqn (2)
squaring on both sides of eqn (1) and then substituting eqn(2) in 1
we get 0.1025+(2/ab)= (0.45*0.45)
(2/ab)= 0.2025-0.1025
(1/ab)=(0.1/2)
ab=20
--> a=(20/b) , substitute this in eqn(1)
(b/20)+(1/b)=0.45
=> b*b - 9*b + 20=0
=>b*b- 5b-4b+20=0
=>b(b-5)-4(b-5)=0
so, b=5 or 4
=> if b=5, a= (20/b) --> a=4
and if b=4, a=5
hence the two numbers are : 4,5

Like? Yes (1) | No (1)  

Harshit Daga   11 years AGO

(1/4)+(1/5)=0.45, and
(1/4)^2 +(1/5)^2=0.1025

Like? Yes (1) | No (1)