Question 74
If $$x^2 + \frac{1}{x^2} = 38$$, then what is the value of $$\mid x - \frac{1}{x} \mid$$?
Solution
$$x^2 + \frac{1}{x^2} = 38$$
$$=$$> $$x^2+\frac{1}{x^2}-2+2=38$$
$$=$$> $$x^2+\frac{1}{x^2}-2.x.\frac{1}{x}+2=38$$
$$=$$> $$\left(x-\frac{1}{x}\right)^2=38-2$$
$$=$$> $$\left(x-\frac{1}{x}\right)^2=36$$
$$=$$> $$\mid x - \frac{1}{x} \mid=6$$
Hence, the correct answer is Option C
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