Question

If a = 2 + V3, find the value ofa --.1/a​

Answer 1

${\underline{\underline{\huge{\mathfrak{\green{Answer:-}}}}}}$

Hey Mate!!

$a=2+\sqrt{3} \\\\=> \frac{1}{a} = \frac{1}{2+\sqrt{3} } \\\\= \frac{2-\sqrt{3} }{(2+\sqrt{3})(2-\sqrt{3}) }\\\\=\frac{2-\sqrt{3}}{2^{2}-(\sqrt{3})^{2} } \\\\=\frac{2-\sqrt{3} }{4-3}\\\\=2-\sqrt{3}\\\\\\=> a+\frac{1}{a}\\\\ =2+\sqrt{3} -(2-\sqrt{3})\\ =2+\sqrt{3}-2+\sqrt{3}\\ =\bold{2\sqrt{3}}$