Question

solve this.This question os of Qudratic Equation​

Answer 1

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$\frac{ \sqrt{1 + x} \: + \sqrt{1 - x} }{ \sqrt{1 + x} - \sqrt{1 - x} } \\ = \frac{( { \sqrt{1 + x} + \sqrt{1 - x} )}^{2} }{ {( \sqrt{1 + x} )}^{2} - {( \sqrt{1 - x} })^{2} } \\ = \frac{1 + x + 1 - x + 2 \sqrt{1 - {x}^{2} } }{1 + x - 1 + x} \\ = \frac{2 + 2 \sqrt{1 - {x}^{2} } }{2x} \\ = \frac{1 + \sqrt{1 - {x}^{2} } }{x} \\ = \frac{1 + \sqrt{1 - ({ \frac{ \sqrt{3} }{2} })^{2} } }{ \frac{ \sqrt{3} }{2} } \\ = \frac{1 + \sqrt{1 - \frac{3}{4} } }{ \frac{ \sqrt{3} }{2} } \\ = \frac{1 + \sqrt{ \frac{1}{4} } }{ \frac{ \sqrt{3} }{2} } \\ = \frac{1 + \frac{1}{2} }{ \frac{ \sqrt{3} }{2} } \\ = \frac{ \frac{3}{2} }{ \frac{ \sqrt{3} }{2} } \\ = \frac{3}{2} \times \frac{2}{ \sqrt{3} } \\ = \sqrt{3}$