Question

If \[\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}={2{1 \over 2}}\] then the value of 'x' are:-

Answer 1

have you tried solving for x?

Answer 2

or is this like a trick question.

Answer 3

Put:

\[\frac{x}{1-x} = y\]

Does it help??

Answer 4

\[Ans: \frac{9}{13} , \frac{4}{13}\]

Answer 5

I tried it but it doesn't work @Romero

Answer 6

you might want to try waterineyes idea.

Answer 7

K!

Answer 8

Put:

\[y = \sqrt{\frac{x}{1-x}}\]

So, it becomes:

\[y + \frac{1}{y} = \frac{5}{2}\]

\[y^2 + 1 = \frac{5}{2}y\]

\[2y^2 - 5y + 2 = 0\]

Calculate y from here by using Quadratic Formula..

Answer 9

Yeah just set it up like a general quadratic equation

Answer 10

\[1 = \frac{x}{1-x}\]

\[1 - x = x\]

\[x = \frac{1}{2}\]

Answer 11

Are you sure the answers are that you given??

Answer 12

2y^2-5y+2=0\[\implies {-(-5)\pm \sqrt{(-5)^2-4(2)(2)}\over 2(2)}\]\[\implies {5\pm \sqrt{25-16} \over 4}\]\[\implies{5\pm \sqrt{9}\over 4}\]\[\implies{5\pm3 \over 4}\]. So, \[\alpha={5+3\over 4}\implies{8 \over 4}=2\] & \[Beta={5-3 \over 4} \implies{2 \over 4}={1 \over 2}\]

Answer 13

Ya! I am 100 & 1 % sure:)

Answer 14

Yes you are right..
It can be solved factorizing:

\[(2y-1)(y-2) = 0\]

\[y = 2 \quad Or \quad y = \frac{1}{2}\]

Answer 15

But wht about my answer:(

Answer 16

@mathslover Plz help:)

Answer 17

We are going absolutely right but I don't know why answer is not right..
The answers you gave that are right..

Answer 18

I also don't know :(
@ParthKohli can u help???

Answer 19

ok wait

Answer 20

k!

Answer 21

@jiteshmeghwal9 ,
There is \(2 \frac{1}{6}\) in the Right Hand Side,



\[y = \sqrt{\frac{x}{1-x}}\]

\[y^2 + 1 = \frac{13}{2}y\]

\[6y^2 - 13y + 6 = 0\]

\[y = \frac{13 \pm \sqrt}{}\]

Using Quadratic Formula:

\[y = \frac{2}{3} \quad Or \quad \frac{3}{2}\]

Now solve for x you will definitely get your answer..

Answer 22

Can u give me total answer:)

Answer 23

Yes why not..

Answer 24

wait i did mistake @waterineyes did i ?

Answer 25

Where??

Answer 26

http://assets.openstudy.com/updates/attachments/4ffc076be4b00c7a70c4c333-mathslover-1341918894923-jitesh.pdf

Answer 27

@waterineyes Plz fast:)

Answer 28

@jiteshmeghwal9 .

The original equation is this:

\[\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}={2{1 \over 6}}\]
If you don't agree then put the answer in this and you can check..

Answer 29

i agree.