If x - 1x - 9- find the value of x2 - 1x2 and x4- 1x4

( x 1x )=9 Squaring on both sides, we get x^2+1x^2=81+2=83 Squaring on both sides, we get x^4+1x^4=6889 2=6887 ...

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(a-b)^2 Expansion and Visualisation

If x - 1x =...

Question

If $x - \frac{1}{x} = 9$ , find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{4} + \frac{1}{x^{4}}$

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x + \frac{1}{x} = - 2

(x^{2} + \frac{1}{x^{2}}) \times

(x^{4} + \frac{1}{x^{4}})

(x + \frac{1}{x}) = 3

x - \frac{1}{x}

x^{2} - \frac{1}{x^{2}}

x^{4} - \frac{1}{x^{4}}

x + \frac{1}{x} = 5

x^{2} + \frac{1}{x^{2}}

x^{4} + \frac{1}{x^{4}}

x + \frac{1}{x} = \sqrt{5}

x^{2} + \frac{1}{x^{2}}

x^{4} + \frac{1}{x^{4}}

If $x + \frac{1}{x} = \sqrt{5}$ , find the values of $x^{2} + \frac{1}{x^{2}} a n d x^{4} + \frac{1}{x^{4}}$ .

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