Question

If a=2+√3 find the value of a-1/a and a+1/a

Answer 1

2+√3-(1/2+√3×2-√3/2-√3) solve this ans will come of yours first ans

2+√3+(1/2+√3×2-√3/2-√3) and this is the hint for second ans hope it helps you

Answer 2

$a = 2 + \sqrt{3} \\ \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } = \frac{2 - \sqrt{3} }{4 - 3} = 2 - \sqrt{3} \\a - \frac{1}{a} = 2 + \sqrt{3} - 2 + \sqrt{3} = 2 \sqrt{3} \: \\ a + \frac{1}{a} = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$