Question

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Answer 1

Question:-

• $\frac{( \sqrt{3} - \sqrt{ 5})( \sqrt{5} + \sqrt{3)} }{7 - 2 \sqrt{5} }$

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$\huge\bold{Solution:-}$

$\implies$$\frac{( \sqrt{3} - \sqrt{5})( \sqrt{5} + \sqrt{3}) }{7 - 2 \sqrt{5} }$

$\implies$$\frac{( \sqrt{3} - \sqrt{5})( \sqrt{3} + \sqrt{5}) }{(7 - 2 \sqrt{5} )}$

$\implies$$\frac{( \sqrt{3} ) {}^{2} - ( \sqrt{5}) {}^{2} }{(7 - 2 \sqrt{5}) } ......Since \: a {}^{2} - b {}^{2} = (a - b)(a + b)$

$\implies$$\frac{3 - 5}{7 - 2 \sqrt{5} } \times \frac{7 + 2 \sqrt{5} }{7 + 2 \sqrt{5} }$

$\implies$ $\frac{ - 2(7 + 2 \sqrt{5}) }{49 - 20} .....Since \: a {}^{2} - b {}^{2} = (a - b)(a + b)$

$\implies$$\frac{ - 14 - 4 \sqrt{5} }{29}$

Hence, solved!

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