Answer # grade9,# algebra,# factorization,#polynomial,#expression

1 answers Answers

PawanScholiber

Factorize:

2021-10-10 10:13:19

: Given x = $3 + 2 \sqrt{2}$

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

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

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

Hence, $x + \frac{1}{x} f o r x = 3 + 2 \sqrt{2}$ is a rational number.

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