Question

solve or question
and should be 0.150150015000.....,0.250250025000​

Answer 1

Answer:

x² + 1/x²  = 322

Step-by-step explanation:

$x = 9 + 4\sqrt{5}$

$\frac{1}{x} = \frac{1}{9 + 4\sqrt{5}}$

Multiplying numerator & Denominator by 9 - 4√5

$\frac{1}{x} = \frac{9 -4\sqrt{5} }{(9+4\sqrt{5} )(9-4\sqrt{5}) } \\\\\frac{1}{x} = \frac{9 -4\sqrt{5} }{(81 - 80) } \\\\\frac{1}{x} = 9 -4\sqrt{5}$

$x^{2} + \frac{1}{x^{2} } = (x + \frac{1}{x})^2 - 2\\\\ x^{2} + \frac{1}{x^{2} } =(9 + 4\sqrt{5} + 9 - 4\sqrt{5} )^2 - 2\\\\ x^{2} + \frac{1}{x^{2} } = 18^2 - 2\\\\ x^{2} + \frac{1}{x^{2} } = 324 - 2\\\\ x^{2} + \frac{1}{x^{2} } = 322$