Question

if X equals to 9 minus 4 root 5 find the value of x to the power 2 + 1 by x to the power 2

Answer 1

$x = 9 - 4 \sqrt{5 } \\ {x}^{2} + \frac{1}{ {x}^{2} } = {x}^{2} + \frac{1}{{x}^{2} } + 2 \times x \times \frac{1}{x} \\ {x}^{2} + \frac{1}{ {x}^{2} } = 81 - 16 \times 5 + \frac{1}{81 - 16 \times 5} + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 81 - 80 + \frac{1}{81 - 80} + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 1 + 1 + 2 = 4$
hope it helps