Question

PawanScholiber

Factorize:

2021-10-10 10:13:19

Jyoti

:     Given x = $3+2\sqrt{2}$

$\frac{1}{x}=\frac{1}{3+2\sqrt{2}}=\frac{1}{3+2\sqrt{2}}x\frac{3-2\sqrt{2}}{3-2\sqrt{2}}$

=$\frac{3-2\sqrt{2}}{{\left(3\right)}^{2}-2\sqrt{2}}=\frac{3-2\sqrt{2}}{9-8}=3-2\sqrt{2}$

$x+\frac{1}{x}=3+2\sqrt{2}+3-2\sqrt{2}=6$  which is a rational number.

Hence, is a rational number.