Question

if X=3-2√2 find the value ofx+1/x

Answer 1

$x = 3 - 2 \sqrt{2}$

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

Rationalise the denominator

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

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

$\frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8}$

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

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

$x + \frac{1}{x} = 6$

Hope it helps