Question

evaluate x^2+1/x^2 when x = 3+root8

Answer 1

Answer:

$x = 3 + \sqrt{8}$

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

now,

${x}^{2} + \frac{1}{ {x}^{2} } = (x + \frac{1}{x} ) {}^{2} - 2 \times x \times \frac{1}{x} = (3 + \sqrt{8} + 3 - \sqrt{8} ) {}^{2} - 2 = {6}^{2} - 2 = 36 - 2 = 34 \: \: ans.$