If -5-x-5-x-5-x-5-x-4- then value of x is

The correct option is D 4017√(5+x)+√(5 x)√(5+x) √(5 x)=4 Applying componendo and dividendo, we get ⇒2√(5+x)2√(5 x)=53 Squaring both sides ⇒5+x5 x=259 ⇒ x=4017 ...

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Standard XII

Mathematics

Vn Method

If √5+x+√5-x/...

Question

If $\frac{\sqrt{5 + x} + \sqrt{5 - x}}{\sqrt{5 + x} - \sqrt{5 - x}} = 4$ , then value of $x$ is

\frac{20}{17}

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\frac{18}{7}

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\frac{40}{17}

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\frac{43}{7}

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Solution

The correct option is C $\frac{40}{17}$
$\frac{\sqrt{5 + x} + \sqrt{5 - x}}{\sqrt{5 + x} - \sqrt{5 - x}} = 4$
Applying componendo and dividendo, we get
$\Rightarrow \frac{2 \sqrt{5 + x}}{2 \sqrt{5 - x}} = \frac{5}{3}$
Squaring both sides
$\Rightarrow \frac{5 + x}{5 - x} = \frac{25}{9}$
$\Rightarrow x = \frac{40}{17}$

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Vn Method

Standard XII Mathematics

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If √5+x+√5−x√5+x−√5−x=4, then value of x is

The correct option is C 4017√5+x+√5−x√5+x−√5−x=4 Applying componendo and dividendo, we get ⇒2√5+x2√5−x=53 Squaring both sides ⇒5+x5−x=259 ⇒x=4017

If $\frac{\sqrt{5 + x} + \sqrt{5 - x}}{\sqrt{5 + x} - \sqrt{5 - x}} = 4$ , then value of $x$ is