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Question

If $x = 5 - 2 \sqrt{6},$ find the value of : ${(x - \frac{1}{x})}^{2}$

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Solution

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Now $\frac{1}{x} = 5 + 2 \sqrt{6}$

Thus the value of $(x - \frac{1}{x})^{2}$ $=$ ((5 - 2 $\sqrt{6}$ ) - (5 + 2 $\sqrt{6})$ ) $^{2}$ $=$ (4\sqrt{6})^2= $16 \times 6$ $=$ $96$

Thus the correct answer is $96$ .

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