Solve {(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2

Akanksha Mishra   10 years AGO

Given;
{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2

[(3x + 1)^2 + (x + 1)^2]/(3x+1)(x+1) = 5/2

(10x^2 + 8x + 2)/(3x^2 + 4x + 1) = 5/2

20x^2 + 16x +4 = 15x^2 +20x + 5

5x^2 - 4x -1 = 0

5x^2 -(5 - 1)x = 0

5x^2 - 5x + x - 1 = 0

5x(x - 1) + 1(x - 1) = 0

5x + 1 = 0
x = -1/5
or

x -1 = 0
x = 1

so answer will be 1,-1/5(option 3)

Like? Yes (19) | No (13)  

shilpi   10 years AGO

solving the equation
x=1 and -1/5

Like? Yes (1) | No   

NAGENDRA P   10 years AGO

let a=3x+1,b=x+1
a/b+b/a=2.5...
a^2+b^2-2.5ab=0..
a^2+b^2-2ab=.5ab...
(a-b)^2=(ab)/2...
by substituting for a and b..
8x^2=3x^2+4x+1....
5x^2-4x-1=0..
by solving the above quadratic equation..
we get x=1,x=-0.2..(-1/5)
so option (3)...

Like? Yes (1) | No   

TINKU MITTAL   10 years AGO

(3x+1)^2+(x+1)^2=(5/2)*(3x+1)*(x+1)
after expanding and rearranging,we get;
5x^2-4x-1=0
(5x+1)(x-1)=0
x=1,-1/5

Like? Yes (1) | No   

viveka   10 years AGO

solving 2{(3x+1)^2(x+1)^2}=5{(3x+1)(x+1)}
5x^2-4x-1=0
-1/5 ,1

Like? Yes (1) | No   

santhosh   10 years AGO

1,-1/5 satisfy the given equation

Like? Yes (1) | No   

Rituparna Chakraborty   10 years AGO

Let, (3x+1)=a
(x+1)=b
then the given equation becomes=
a/b+b/a=5/2
=>2a^2-5ab+2b^2=0
=>2a^2-4ab-ab+2b^2=0
=>(a-2b)(2a-b)=0
So,(a-2b)=0
putting the value of a,b we obtain,
=>(3x+1)-2(x+1)=0
=>x=1
and (2a-b)=0
putting the value of a,b we obtain,
=>2(3x+1)-(x+1)=0
=>x=-1/5
S0,x=1,-1/5

Like? Yes (1) | No   

Mahalakshmi   10 years AGO

solving this equation i get 5x^2-4x-1=0
solving it
x=1,-1/5

Like? Yes (1) | No   

Vaishali Dhiman   10 years AGO

option is 3
{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
{(3x+1)^2+(x+1)^2}/{(3x+1)(x+1)}=5/2
{9x^2+1+6x+x^2+1+2x}/{3x^2+4x+1}=5/2
{10x^2+8x+2}/{3x^2+4x+1}=5/2
20x^2+16x+4=15x^2+20x+5
5x^2-4x-1=0
5x^2-5x+x-1=0
5x(x-1)+1(x-1)=0
(5x+1)(x-1)=0
x=(-1/5),1

Like? Yes (1) | No   

neeraj   10 years AGO

3x+1/x+1=x+1/3x+1=5/2
(3x+1)^2+(x+1)^2/x+1*3x+1=5/2
solve the equation x=1 and x=-1/5

Like? Yes (1) | No   

ranu   10 years AGO

3x+1/x+1=x+1/3x+1=5/2
(3x+1)^2+(x+1)^2/x+1*3x+1=5/2
solve the equation x=1 and x=-1/5

Like? Yes (1) | No   

Vijit Mangla   10 years AGO

{(3x+1)2+(x+1)2}/{(3x+1)(x+1)}=5/2
10x2+8x+2/3x2+4x+1=5/2
20x2+16x+4/3x2+4x+1=5/2
5x2-4x-1=0
x= 4+_{(36)1/2}/10
x=1,-1/5

Like? Yes (1) | No   

PAYAL GAUTAM   10 years AGO

let a=3x+1 & b=x+1
2(a^2)+2(b^2)-5ab=0
=> a=b/2 or a=2b
=> 3x+1=(x+1)/2 or 3x+1=2*(x+1)
=> x=-1/5 or x=1

Like? Yes (1) | No   

Vijaya Bharathi   10 years AGO

Solve equation,
We get X=1
X=-1/5

Like? Yes (1) | No   

techknowxpress   10 years AGO

2*((3x+1)^2+(x+1)^2)-5*((x+1)*(3x+1))=0
therefore, 5x^2-4x-1=0
solving we get,
x=1,(-1/5)

Like? Yes (1) | No   

Aditya Verma   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
2{(3x+1)^2+(x+1)^2}=5{(3x+1)(x+1)}
=>5x^2-4x-1=0
=>x=1,-1/5(answer)

Like? Yes (8) | No (9)  

chethan   10 years AGO

by solving the equation,we ll get d answer..

Like? Yes (1) | No (4)  

komathi rajan   10 years AGO

answer is simple. on simplification of the equation by squaring,expanding and furthur calculation. we get the answer as x=1 or x=(-1/5)

Like? Yes (1) | No (4)  

Parthi Smith   10 years AGO

[((3*1)+1)/(1+1)]+[(1+1)/((3*1)+1)]=5/2
[((3*(-1/5)+1)/(1+1)]+[((-1/5)+1)/(3*(-1/5)+1)]=5/2

Like? Yes (1) | No (4)  

karthik hariharan   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)}=5/2

(3x+1)^2+(x+1)^2/(x+1)(3x+1)=5/2

10x^2+8x+2/3x^2+4x+1=5/2

20x^2+16x+4=15x^2+20x+5
5x^2-4x-1=0
x=1,-1/5

Like? Yes (1) | No (4)  

Jigyasa Kumar   10 years AGO

on solving the equation 5x^2-4x-1=0
we get the roots x=1,-1/5

Like? Yes (2) | No (5)  

abhilasha   10 years AGO

on solving the equation 5x^2-4x-1=0
we get the roots x=1,-1/5

Like? Yes (2) | No (5)  

RAKESH   10 years AGO

(3x+1)/(x+1)=y then
y+ 1/y = 5/2
=>(y-2)(2y-1)=0
=> y=2, 1/2
so, (3x+1)/(x+1)= 2, 1/2 => x=1,-1/5

3) x = 1, x = -1/5

Like? Yes (4) | No (8)  

saurabh   10 years AGO

3x+1/x+1 + x+1/3x+1 =5/2
by taking LCM
(3x+1)(3x+1)+(x+1)(x+1)/(x+1)(3x+1)=5/2------1
by solving equation 1 and cross multiplication
we get
20x^2+16x+4=15x^2+20x+5
20x^2-15x^2+16x-20x+4-5=0
5x^2-4x-1=0
5x^2-5x+x-1=0
5x(x-1)+(x-1)=0
(x-1) (5x+1)-----------------2
by equating equation 2 with 0
we get
x-1=0 , x=1
and 5x+1=0 , x=-1/5

hence x=1,-1/5

Like? Yes (2) | No (6)  

ASHISH MITTAL   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
let 3x+1=a and x+1=b
so equation become
(a/b)+(b/a)=(5/2)
after solving this equation we get
2a=b and a=2b
so after putting value of a and b we get
x=-1/5 and x=1

Like? Yes (1) | No (5)  

roshani munde   10 years AGO

put 3x+1=p & x+1=q then solve fr p & q

Like? Yes (1) | No (5)  

Snehasis   10 years AGO

Given,
{(3x+1)/(x+1)} + {(x+1)/(3x+1)} = 5/2

Take LCM in left hand side then,
(3x+1)^2 + (x+1)^2/(x+1)(3x+1) = 5/2

Now, using [(a+b)^2 = a^2+b^2+2ab] formula for the LHS(left hand side) numerator,
we get,

9x^2 + 1 + 6x + x^2 + 1 + 2x/(x+1)(3x+1) = 5/2

now, open the brackets of the denominator and solve the numerator, we get,

10x^2 + 8x + 2/3x^2 + 4x + 1 = 5/2

Applying cross-multiplication to the above equation,

20x^2 + 16x +4 = 15x^2 + 20x + 5

Bringing all the right hand side(RHS) term to LHS and solving them,

5x^2 - 4x - 1 = 0

Now, Applying middle term factorization to the above equation then,

5x^2 - 5x + x - 1 = 0

=> 5x(x-1) + 1(x-1) = 0

=> (5x+1)(x-1) = 0

Now solving the equations separately,

5x+1=0 and, x-1=0

=> x = -1/5 => x = 1

The required quadratic root values of x are:

x = 1 and x = -1/5.

Like? Yes (3) | No (7)  

ganesh saicharan rao   10 years AGO

a+1/a=5/2
=2+1/2
->a=2or1/2
3x+1=2(x+1) or 2(3x+1)=x+1
x=1 x=-1/5

Like? Yes (1) | No (5)  

aviral bhargava   10 years AGO

on solving above equation we get,
2(10x^2+8x+2)=5(3x^2+4x+1)
=>5x^2-4x-1=0
Leading to the values of 1 and -1/5.
Hence the option 3rd is correct

Like? Yes (2) | No (6)  

MADHU   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)}=5/2
=> [(3x+1)^2 + (x+1)^2]/[(3x+1)(x+1)]=5/2
=> 5x^2-4x-1=0
=> x=1,-1/5
so ans is 3rd option.

Like? Yes (1) | No (5)  

pari   10 years AGO

let M=(3x+1)/(x+1) n put it in eq.

so we get M+1/M=5/2 -- (I)

solve this eq. u will get M=2,1/2

now put real value of M
like (3x+1)/(x+1)=2 and (3x+1)/(x+1)=1/2

so we wil get x= 1 and -1/5

Like? Yes (1) | No (5)  

Satish Zod   10 years AGO

{(3x+1)/(x+1)} + {(x+1)/(3x+1)} = 5/2
Solving this,
(10x^2 + 8x + 2) / (3x^2 + 4x + 1) = 5/2
5x^2 - 4x – 1 = 0
a= 5, b= - 4, c= - 1

x = [4 ± √(16 + 20)] / 10
x= 1
x= -1/5

Like? Yes (1) | No (5)  

SIVA BALSUBRAMANIAN   10 years AGO

by solving the question we get final quation as
5x^2-4x-1=0
from that
x=1,-1/5

Like? Yes (1) | No (5)  

julee verma   10 years AGO

(3x+1)^2+(x+1)^2/(3x+1)(x+1)=5/2
9x^2+1+6x+x^2+1+2x/(3x^2+3x+x+1)=5/2
2*(10x^2+8x+2)=5*(3x^2+4x+1)
20x^2+16x+4=15x^2+20x+5
5x^2-4x-1=0
5x^2-5x+x-1=0
(5x+1)(x-1)=0
x=-1/5,x=1

Like? Yes (1) | No (5)  

Anand Kumar Saini   10 years AGO

Equation will become :5x^2-4x-1=0
solution of this eq.
5x^2-5x+x-1=0
5x(x-1)+(x-1)=0
(5x+1)(x-1)=0
so result will be:x=1,x=-1/5

Like? Yes (1) | No (5)  

shamma mohammad   10 years AGO

Option cheking:3
By substituting ‘x’ values in the equation we get 5/2
The values satisfy dis eqn is
x=1,x=-1/5

Like? Yes (1) | No (5)  

Prashasti Sharma   10 years AGO

(3x+1)^2 + (x+1)^2=5/2(3x+1)(x+1)
5x^2-4x-1=0
on solving x=1 and x=-1/5

Like? Yes (1) | No (5)  

basha shaik   10 years AGO

Wen we solve dis eqn,we get
5x^2-4x-1=0
roots for abov eqn are
x=1,x=-1/5

Like? Yes (1) | No (5)  

sowmya   10 years AGO

option verification so ans is x=1 & x=-1/5

Like? Yes (1) | No (5)  

Ashish Bhandari   10 years AGO

only x=1 and x=-1/5 is satisfy this equation

Like? Yes (2) | No (6)  

IFFAT IRAM   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
2{(3x+1)^2+(x+1)^2}=5{(3x+1)(x+1)}
2(10x^2+2+8x)=5(3x^2+1+4x)
5x^2-4x-1=0
(5x+1)(x-1)=0
x=1 or -1/5

Like? Yes (1) | No (5)  

Rakesh Kumar Kohli   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
=>2*[{(3x+1)^2+{(x+1)^2] = 5*(3x+1)*(x+1)
=>2*[{(3x+1-x-1)^2] = (3x+1)*(x+1)
=>8x^2 = 3x^2+4x+1
=>5x^2-4x-1=0
=>(5x+1)*(x-1)=0
=> x = -1/5 OR 1 which is option 3).

Like? Yes (1) | No (5)  

Aarush Singh   10 years AGO

on solving the equation 5x^2-4x-1=0
we getthe roots x=1,-1/5

Like? Yes (1) | No (5)  

Shiksha gautam   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
(3x+1)/(x+1) =(5/2)-{(x+1)/3x+1}
(3x+1)/(x+1)=(13x+3)/(6x+2)
5x^2-4x-1=0
5x^2-5x+x-1=0
5x(x-1)+1(x-1)=0
(5x+1)(x-1)=0
x=1,x=-1/5

Like? Yes (1) | No (5)  

Varunraj Reddy   10 years AGO

Simplifying the given equation becomes
5x^2-4x-1=0
By solving we get
x=1,-1/5 option 3.

Like? Yes (1) | No (5)  

Hemalatha   10 years AGO

on solving,
5x^2-4x-1=0;x=1,-1/5

Like? Yes (1) | No (5)  

vasudha   10 years AGO

{(3x+1)/(x+1)}+{(x+1)/(3x+1)} = 5/2
by taking L.C.M,
{(3x+1)^2+(x+1)^2}/{(3x+1)*(x+1)}=5/2
by using (a+b)^2=a^2+b^2+2ab
we get (9x^2+1+6x+x^2+2x+1)/(3x^2+4x+1) = 5/2
i.e.,
{(10x^2+8x+2)/(3x^2+4x+1)}=5/2
by cross multiplication,
20x^2+16x+4=15x^2+20x+5
by simplifying above equation we get,
5x^2-5x-1=0
by finding the roots of the equation we get x=1,x=-1/5

Like? Yes (1) | No (5)  

tejaswini   10 years AGO

by considering (3x+1)/(x+1)=x
so x+(1/x)=5/2
by solving this equation we get x=2,1/2
again by substituting in x value
we get x=1,-1/5

Like? Yes (1) | No (5)  

SIBNATH HALDER   10 years AGO

{(3x+1)^2+(x+1)^2}/(x+1)(3x+1)=5/2,
(10x^2+8x+2)/(3x^2+4x+1)=5/2,
20x^2+16x+4=15x^2+20x+5,
5x^2-4x-1=0,
(5x+1)(x-1)=0,
x=1,x=-1/5;

Like? Yes (1) | No (5)  

sravan   10 years AGO

by solving above eqation you will get
5x^2-4x-1=0
5x^2-5x+x-1=0
5x(x-1)+1(x-1)=0
so the roots are x=1,x=-1/5

Like? Yes (1) | No (5)  

VIKASH RAY   10 years AGO

by,solving the given equation we get the following answer..

Like? Yes (1) | No (5)  

ARJYA HALDER   10 years AGO

Let, [(x+1)*(3*x+1)]=a
Then the equation becomes, a+(1/a)=(5/2)
Solving the equation we get, a=2 & a=(1/2)
a=2 gives x=(-1/5) &
a=(1/2) gives x=1
So, option 3 is correct.

Like? Yes (1) | No (5)  

Gudivada sunitha   10 years AGO

substitute the options. by substituting 3 option
(3*1+1)/(1+1)+(1+1)/(3*1+1)=4/2+2/4= 2+1/2= 5/2

Like? Yes (1) | No (5)  

SONU GUPTA   10 years AGO

answer will be x=1, x=-1/5

Like? Yes (1) | No (6)