Question

Rationalise it:
1+√2/2-√2



Answer is :__4+3√2/2______
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Answer 1

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RATIONALISE

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$\frac{1 + \sqrt{2} }{2 - \sqrt{2} } \\ \\ = \geqslant \frac{1 + \sqrt{2} }{2 - \sqrt{2} } \times \frac{2 + \sqrt{2} }{2 + \sqrt{2} } \\ \\ = \geqslant \frac{2 + \sqrt{2} + 2 \sqrt{2} + 2}{ {2}^{2} - \sqrt{2} {}^{2} } \\ \\ = \geqslant \frac{4 + 3 \sqrt{2} }{4 - 2} \\ \\ = \geqslant \frac{4 + 3 \sqrt{2} }{2}$

Answer 2

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