Question

a=2+ V3, then find the value of (a-1/a)​

Answer 1

Given,

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

To Find : a - 1/a = ?

@---@ SOLUTION @---@

Here,

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

Then,

$\rm\frac{1}{a} = \frac{1}{2 + \sqrt{3} } \\ \\ \to\frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \to \frac{1(2 - \sqrt{3} )}{ {(2)}^{2} - {( \sqrt{3} )}^{2} } \\ \\ \to \frac{2 - \sqrt{3} }{4 - 3} = \frac{2 - \sqrt{3} }{1} \\ \\ \tt \implies \frac{1}{a} = 2 - \sqrt{3}$

Now,

$\bf{}a - \dfrac{1}{a} = 2 + \sqrt{3} - (2 - \sqrt{3} ) \\ \\ \tt{}a - \dfrac{1}{a} \: \: \to \: \: 2 + \sqrt{3} - 2 + \sqrt{3} \\ \\ \tt{}a - \dfrac{1}{a} \: \: \to \: \: \: \red{2 \sqrt{3} }$

Thus,

• Required value of a - 1/a = 2√3