1.

If \(x=\frac{{\sqrt 3 }}{2}\), then the value of \(\frac{{\sqrt {1 + x} + \sqrt {1 - x} }}{{\sqrt {1 + x} - \sqrt {1 - x} }}\) is equal to:1. √22. √33. 34. 2

Answer» Correct Answer - Option 2 : √3

Calculation:

\({√(1 + x) + √(1 – x)}\over{√(1 + x) – (√1 – x)}\) × \({√(1 +x) + √(1 – x)}\over {√(1 + x) + √(1 – x)}\)

⇒ \((1 + x) + (1 – x) + 2√(1 – x^2) \over(1 + x) – (1 – x)\)

⇒ \(2 + 2√(1 – (√3/2)^2)\over2x\)

⇒ \(2 + 2 × (1/2)\over 2 × (√3/2) \)

⇒ (3/√3) × (√3/√3)  

⇒ √3   


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