Question

if a=2+√3, then a + 1/a is equal to​

Answer 1

Given :-

$→a = 2 + \sqrt{3}$

$\rule{200}{1}$

Solution -

$</strong><strong>→</strong><strong>a + \frac{1}{a}$

$</strong><strong>→</strong><strong>(2 + \sqrt{3} ) + \frac{1}{(2 + \sqrt{3}) } \\ \\</strong><strong>→</strong><strong> \frac{(2 + \sqrt{3})(2 + \sqrt{3}) + 1 }{2 + \sqrt{3} } \\ \\ </strong><strong>→</strong><strong> \frac{( {2 + \sqrt{3} )}^{2} + 1}{2 + \sqrt{3} } \\ \\</strong><strong>→</strong><strong> \frac{4 + 3 + 2 \times 2 \sqrt{3} + 1 }{2 + \sqrt{3} } \\ \\ </strong><strong>→</strong><strong>\frac{8 + 4 \sqrt{3} }{2 + \sqrt{3} } \\ \\ </strong><strong>→</strong><strong>\frac{4(2 + \sqrt{3}) }{(2 + \sqrt{3} )} \\ \\ </strong><strong>\</strong><strong>b</strong><strong>o</strong><strong>x</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>→</strong><strong>4</strong><strong>}</strong><strong>$

$\rule{200}{1}$

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