Question

Solve (√x/1-x)+(√1-x/x)=13/6

Answer 1

Step-by-step explanation:

Here, the given expression,

\sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6}

\frac{\sqrt{x}}{\sqrt{1-x}}+\frac{\sqrt{1-x}}{\sqrt{x}}=\frac{13}{6}

\frac{x+1-x}{\sqrt{x(1-x)}}=\frac{13}{6}

\frac{1}{\sqrt{x(1-x)}}=\frac{13}{6}

6=13[\sqrt{x(1-x)}]

By squaring both sides,

36=169[x(1-x)]

36=169x-169x^2

169x^2-169x+36=0

By splitting the middle term,

169x^2-117x-52x+36=0

13x(13x-9)-4(13x-9)=0

(13x-9)(13x-4)=0

\implies 13x - 9 = 0\text{ or }13x - 4 = 0

\implies x = \frac{9}{13}\text{ or }x = \frac{4}{13}

Which is the required solution.

Answer 2

Answer :

x=9/13 or x=4/13