Question

If a=2+√3 then a-1/a is equal to
2√3
4
2+√3
none of these​

Answer 1

Given,

$\sf{a = 2 + \sqrt{3}}$

To find,

the value of $\sf{a-\frac{1}{a}}$.

Solution,

Putting the value of $\sf{a = 2 + \sqrt{3}}$ in $\sf{a-\frac{1}{a}}$.

$\implies\sf{2 +\sqrt{3}-\frac{1}{ 2 +\sqrt{3}}}$

Rationalising the denominator,

$\implies\sf{2 + \sqrt{3} - \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }}$

$\implies\sf{2 + \sqrt{3} - \frac{2 - \sqrt{3} }{(2)^{2} - (\sqrt{3}) ^{2}}}$

$\implies\sf{2 + \sqrt{3} - \frac{2 - \sqrt{3} }{4 - 3}}$

$\implies\sf{2 + \sqrt{3} - (2 - \sqrt{3})}$

$\implies\sf{\cancel{2}+1\sqrt{3}\cancel{ -2}+1\sqrt{3}}$

$\implies\sf{1\sqrt{3}+1\sqrt{3}}$

$\implies\sf{2\sqrt{3}}$

$\implies{\sf{\boxed{a - \frac{1}{a} = 2 \sqrt{3}}}}$

Hence, If a=2+√3 then a-1/a is equal to 2√3.