Question

plz answer this question ​

Answer 1

Answer:

$\frac{ \sqrt{a + x} + \sqrt{a - x} }{ \sqrt{a + x} - \sqrt{a - x} } = b \\ \frac{ {( \sqrt{a + x} + \sqrt{a - x}) }^{2} }{a + x - a + x} = b \\ a + x + a - x + 2 \sqrt{ {a}^{2} - {x}^{2} } = 2bx \\ 2a + 2 \sqrt{ {a}^{2} - {x}^{2} } = 2bx \\ a + \sqrt{ {a}^{2} - {x}^{2} } = bx \\ \sqrt{ {a}^{2} - {x}^{2} } = bx - a \\ {a}^{2} - {x}^{2} = {b}^{2} {x}^{2} + {a}^{2} - 2abx \\ {b}^{2} {x}^{2} + {x}^{2} = 2abx \\ {x}^{2} ( {b}^{2} + 1) = 2abx \\ x( {b}^{2} + 1) = 2ab \\ x = \frac{2ab}{ {b}^{2} + 1 }$