Question

pls solve this question


4+√5/4-√5​

Answer 1

$\huge\color{blue}{\mid{\fbox{\tt{Solution}}\mid}}$

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$\huge\sf\underline\red{Identities\:to\:use}$

$\small\fbox\pink{a²-b²= (a+b) (a-b)}$

$\small\fbox\pink{(a+b)²= a²+2ab+b²}$

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } \\ \\ = \frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } \\ \\ = \frac{(4 + \sqrt{5}) {}^{2} }{(4) {}^{2} - ( \sqrt{5} ) {}^{2} } \\ \\ = \frac{16 + 5 + 2(4 \times \sqrt{5}) }{16 - 5} \\ \\ = \frac{16 + 5 + 8 \sqrt{5} }{11} \\ \\ = \frac{21 + 8 \sqrt{5} }{11}$

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