Question

if x=9-4root5 , find the value of x square + 1/x square

Answer 1

We rationalize the value of 1/x and then square it before adding. if equations do not display properly, try REFRESHing the browser.

[tex] x = 9 - 4 \sqrt{5} \\ \\ 1/x = \frac{1}{9-4\sqrt{5}} = \frac{9+4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})} \\ \\ \frac{9+4\sqrt{5}}{9^2 - (4\sqrt{5})^2} \\ \\ \frac{9+4\sqrt{5}}{81 - 80} \\ \\ 9 + 4 \sqrt{5} \\ [/tex]

$x^{2} = 9^2 + 4^2 \sqrt{5}^2 - 2 * 9 * 4 * \sqrt{5} = 81+80-72\sqrt{5} \\ \\ \frac{1}{x^2} = (9+4\sqrt{5})^2 = 9^2+4^2\sqrt{5}^2 + 2 * 9 * 4 * \sqrt{5} = 81 + 80 + 72 \sqrt{5} \\ \\ x^2 + \frac{1}{x^2} = 161*2 = 322$

Answer 2

Answer : 322 ..

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