Question

Solve this question with explanation
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Answer 1

SOLUTION.

Given to evaluate –

$\tt = \sqrt{2 {x}^{2} - 1 + 2x \sqrt{ {x}^{2} - 1} }$

On rearranging the terms inside square root, we get,

$\tt = \sqrt{({x}^{2}) + ({x}^{2} - 1) + 2x \sqrt{ {x}^{2} - 1} }$

Now, we can rewrite this as,

$\tt = \sqrt{{(x)}^{2} + (\sqrt{ {x}^{2} - 1})^{2} + 2 \times x \times \sqrt{ {x}^{2} - 1} }$

Which gives us the formula of (a + b)². Using formula, we get,

$\tt = \sqrt{ {(x + \sqrt{ {x}^{2} - 1 } )}^{2} }$

$\tt = x + \sqrt{ {x}^{2} - 1 }$

Which is our required answer.

★ So, option b is the correct answer for the question.

ANSWER.

• Option B.