Question

Solve this urgent h Please​

Answer 1

Answer:

$\large\bold\red{x = \frac{5}{4}}$

Explanation:

Given,

$\frac{ \sqrt{x + 1} + \sqrt{x - 1} }{ \sqrt{x + 1} - \sqrt{x - 1} } = \frac{4x - 1}{2}$

Applying componendo amd dividendo,

we get,

$= > \frac{ \sqrt{x + 1} }{ \sqrt{x - 1} } = \frac{4x + 1}{4x - 3} \\ \\ = > \frac{x + 1}{x - 1} = \frac{16 {x}^{2} + 8x + 1}{16 {x}^{2} - 24x + 9}$

Again,

applying componendo and Dividendo,

we get,

$= > \frac{2x}{2} = \frac{32 {x}^{2} - 16x + 10 }{32x - 8} \\ \\ = > x = \frac{16 {x}^{2} - 8x + 5 }{16x - 4} \\ \\ = > 16 {x}^{2} - 4x = 16 {x}^{2} - 8x + 5 \\ \\ = > x = \frac{5}{4}$

Hence,

$\large\bold{x=\frac{5}{4}}$

Answer 2

Answer:

x=5/4

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