Question

CAN YOU SOLVE IT ??


FULL SOLUTION PLEASE.

Answer 1

This way it can be solved

Answer 2

HLO MATE !!!!

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$= > a = \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \: \: \: \: b = \frac{2 + \sqrt{5} }{2 - \sqrt{5} } \\ \\ find \: a {}^{2} - b {}^{2} \\ \\ first \: rationalise \: \: a \: \: \\ a = \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ \\ a = \frac{(2 - \sqrt{5} ) {}^{2} }{(2 {}^{2} - \sqrt{5} {}^{2} ) } \\ \\ a = \frac{4 + 5 - 4 \sqrt{5} }{4 - 5 } \\ \\ a = \frac{9 - 4 \sqrt{5} }{ - 1} \\ \\ a = - 9 - 4 \sqrt{5} \\ \\ now \: rationalise \: b \: \\ b = \frac{2 + \sqrt{5} }{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} } \\ \\ b = \frac{(2 + \sqrt{5}) {}^{2} }{2 {}^{2} - \sqrt{5} {}^{2} } \\ \\ b = \frac{4 + 5 + 4 \sqrt{5} }{4 - 5} \\ \\ b = \frac{9 + 4 \sqrt{5} }{ - 1} \\ \\ b = - 9 + 4 \sqrt{5} \\ \\ so \\ a {}^{2} - b {}^{2} = ( - 9 - 4 \sqrt{5} ) { }^{2} - ( - 9 + 4 \sqrt{5}) {}^{2} \\ = > (81 + 80 - 72 \sqrt{5} ) - (81 + 80 + 72 \sqrt{5} ) \\ = > 161 - 72 \sqrt{5} - 161 - 72 \sqrt{5} \\ = > - 144 \sqrt{5}$

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