Question

x=3+root8,find x^2+1/x^2​

Answer 1

Answer:

79

Step-by-step explanation:

$x = 3 + \sqrt{8} \\ \\ \frac{1}{x} = \frac{1}{(3 + \sqrt{8}) } \times \frac{(3 - \sqrt{8} )}{(3 - \sqrt{8} )} \\ \\ = \frac{3 - \sqrt{8} }{ {3}^{2} - { \sqrt{8} }^{2} } = 3 - \sqrt{8} \\ \\ (x + \frac{1}{x} ) = (3 + \sqrt{8}) + (3 - \sqrt{8} ) \\ = 9 \\ \\ {(x + \frac{1}{x} }^{2}) = {9}^{2} = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 81 - 2 = 79$