Question

If x = 3 + 2√2 then check whether x-1/x is rational or irrational

Answer 1

Answer: After solving it we get

X-1\x=2√2-2

which is irrational

Hence,it a irrational number

Answer 2

$Given \:x = 3+2\sqrt{2}\: ---(1)$

$\frac{1}{x} = \frac{1}{3+2\sqrt{2}}\\= \frac{3-2\sqrt{2}}{(3-2\sqrt{2})</p><p>(3+2\sqrt{2})}\\= \frac{3-2\sqrt{2}}{3^{2} - (2\sqrt{2})^{2}}\\= \frac{3-2\sqrt{2}}{9- 8}\\= 3-2\sqrt{2} \: --(2)$

$Now , x - \frac{1}{x} \\= 3+2\sqrt{2} - (3-2\sqrt{2})\\= 3+2\sqrt{2} - 3+2\sqrt{2}\\= 4\sqrt{2} \: \pink {( Irrational )}$

Therefore.,

$\red{x - \frac{1}{x}} \green { = 4\sqrt{2} \: \pink {( Irrational )}}$

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