Question

√(x+4)+√(x-4) /√(x+4)-√(x-4)=2 then find the value of x​

Answer 1

Answer:

$\frac{17}{4}$

Step-by-step explanation:

Multiply both Numerator and Denominator with $\sqrt{x + 4} + \sqrt{x - 4}$

You will get $\frac{ ({ \sqrt{x + 4} + \sqrt{x - 4} ) }^{2} }{x + 4 - x + 4} = 2$

$({ \sqrt{x + 4} + \sqrt{x - 4} ) }^{2} = 16$

$x + 4 + x - 4 + 2 \sqrt{ {x}^{2} - 4 } = 16$

$x - 8 = \sqrt{ {x}^{2} - 4 }$

Squaring on both sides we will get

${x}^{2} + 64 - 16x = {x}^{2} - 4$

$16x = 68$

So, $x = \frac{68}{16} = \frac{17}{4}$

So, $x = \frac{17}{4}$