Question

Solve for 'x'...question in comment

Answer 1

\[\sqrt{\frac{ x }{ 1 - x }} + \sqrt{1 - x} = \frac{ 5 }{ 2 }\]

Answer 2

I believe you have squared both sides n have tried to get the solution

Answer 3

give a try ...not gonna really work...gets more complicated .. @rvc

Answer 4

@butterflydreamer

Answer 5

try square both sides:
\[\frac{ x }{ 1-x }+2*\sqrt{\frac{ x }{ 1-x }*(1-x)}+(1-x)=\frac{ 25 }{ 4 }\]
\[\frac{ x }{ 1-x }+2*\sqrt{x}+1-x=25/4\]
try solving this

Answer 6

tried got complicated though

Answer 7

Wouldn't it just become \[\frac{ x }{ 1-x } + (1-x) = \frac{ 25 }{ 4 }\]
Which it pretty easy to solve

Answer 8

(a + b)^2 = a^2 + b^2 + 2ab @Utterly_Confuzzled

Answer 9

it will be easy but it will be wrong

Answer 10

Oh right, completely slipped my mind!

Answer 11

it happens

Answer 12

i ran out of ideas

Answer 13

umm if u consider \[\sqrt{1 - x} = t\]
then x = 1 - t^2

Answer 14

so how is it possible tht
\[\sqrt{x} = \sqrt{1 - t}\]

Answer 15

\[\sqrt{\frac{ x }{ t }}+\sqrt{t}=5/2\]

Answer 16

hmm

Answer 17

@AlexandervonHumboldt2 lol we got kinda two variables now

Answer 18

yeah this is a tricky problem


why ganehise is not online? he would do this in a second

Answer 19

lol......xD

Answer 20

I can only say
x is in (0,1)

Answer 21

No integral value satisfying x.

Answer 22

yup the same i got ........

Answer 23

I'm getting √x=-1/(1-x)
When try to find this function's maximum value. So its undefined.

Answer 24

\(\rm\frac{ x }{1-x }+2\sqrt{(1-x)\frac{ x }{ 1-x }}+(1-x)=25/4\\\frac{ x }{1-x }+2\sqrt{ x}+(1-x)=25/4\\~\\let~1-x=t~;x=1-t~;\sqrt{x}=\sqrt{1-t}\\ \frac{ 1-t }{t } +2\sqrt{1-t}+t=25/4\\~(1-t)+2\sqrt{1-t}\cdot~t+t^2=\frac{ 25 }{ 4 } t\\~([\sqrt{1-t}]+t)^2=(\frac{ 5\sqrt{t} }{2 })^2\)

Answer 25

omg

Answer 26

\[\infty ~~~medals~\to~rvc\]

Answer 27

haha

Answer 28

@freckles please help :)

Answer 29

@Kainui help buddy

Answer 30

Where did you get this problem, are you sure it's right?

Answer 31

I don't think this has a simple closed form solution. I am thinking you're supposed to approximate the solution with like Newton's method or something here.

Answer 32

My guess was to try to make it sorta symmetric by dividing the original equation by \(\sqrt[4]{x}\) like this:

\[\left( \frac{(1-x)^{1/2}}{x^{1/4}} \right)^{-1} + \frac{(1-x)^{1/2}}{x^{1/4}} = \frac{5}{2 x^{1/4}}\]
But I don't think that really helps us at all lol.

Answer 33

hahaha
nice try though

Answer 34

I would like to know if the problem is written correctly too... and if so I wondering about further instructions such as approximation x by some method

Answer 35

@rvc its a qestion asked in UPSC exam

Answer 36

and i cant recall the options .....bt they all were improper fractions

Answer 37

@freckles we can do this by any method
we require the value of x

Answer 38

http://www.wolframalpha.com/input/?i=%E2%88%9A%28x%2F%281-x%29%29%2B%E2%88%9A%281-x%29%3D5%2F2