Question

√x/1–x +√1–x/x =13/16​

Answer 1

$\huge{\red{\fbox{\red{\fbox{\green{Given\; Question\;is\; incorrect}}}}}}$

Correct question is ,

$\sqrt{\dfrac{x}{1-x}}+\sqrt{\dfrac{1-x}{x}}=\dfrac{13}{6}$

$\huge{\red{\fbox{\purple{\underline{\blue{Answer:}}}}}}$

• $\sqrt{\dfrac{x}{1-x}}+\sqrt{\dfrac{1-x}{x}}=\dfrac{13}{6}$

• $\dfrac{\sqrt{x^2}+\sqrt{(1-x)^2}}{\sqrt{x(1-x)}}=\dfrac{13}{6}$

• $\dfrac{x+1-x}{\sqrt{x(1-x)}}=\dfrac{13}{6}$

• $\dfrac{1}{\sqrt{x(1-x)}}=\dfrac{13}{6}$

• $\dfrac{6}{\sqrt{x(1-x)}}=13$

• $\dfrac{\sqrt{36}}{\sqrt{x(1-x)}}=13$

• $\dfrac{36}{x(1-x)}=13^2$

• 169x(1-x) = 36

• 169x - 169x² -36 = 0

• 169x² - 169x + 36 = 0

• 169x² - 52x -117x + 36 = 0

• 13x(13x-4) - 9(13x-4) = 0

• (13x-9)(13x-4) = 0

Therefore the required values of x are

$\red{\fbox{\green{x=\dfrac{9}{13}\;and\;\dfrac{4}{13}}}}$

Answer 2

Answer:

I think the question is like this............

√ ( x / 1- x) + √ ( 1 - x /x ) = 13/16

{(√x * √x ) + ( √1 -x * √ 1 - x)  }/ {√(1 - x ) x } = 13 /16

(x + 1 - x ) / {√(1 - x ) x } = 13/16

1/{√(1 - x ) x }=13/16

16 = 13 {√(1 - x ) x }

16/13 ={√(1 - x ) x }

squaring on both sides 

256/169 = (1 - x ) x

            = x - x^2

x^2 - x + 256/169 =0

169x^2 - 169x +256 = 0 

x = 1/2   - 3√95 /26 i   , 1/2   + 3√95 /26 i (answer )

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