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if x = 3- 2_root2 then find the value of oh x⁴ - 1/x⁴

$Given x = 3 - 2 \sqrt{2} \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}} = \frac{3 + 2 \sqrt{2}}{9 - 8} = 3 + 2 \sqrt{2} x + \frac{1}{x} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} = 6 x - \frac{1}{x} = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} = - 4 \sqrt{2} (x + \frac{1}{x}) (x - \frac{1}{x}) = (x^{2} - \frac{1}{x^{2}}) = 6 \times - 4 \sqrt{2} = - 24 \sqrt{2} (x + \frac{1}{x})^{2} = x^{2} + \frac{1}{x^{2}} + 2 = 36 \Rightarrow x^{2} + \frac{1}{x^{2}} = 34 x^{4} - \frac{1}{x^{4}} = (x^{2} + \frac{1}{x^{2}}) (x^{2} - \frac{1}{x^{2}}) = (34) (- 24 \sqrt{2}) = - 816 \sqrt{2}$

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