Question 40

If $$a^2 + \frac{1}{a^2} = 51$$, $$a > 1$$, then the value of $$a - \frac{1}{a}$$ is

Solution

We have $$\left(a - \frac{1}{a}\right)^2 = a^2 + \frac{1}{a^2} - 2 = 51 - 2 = 49$$. Since $$a > 1$$, $$a - \frac{1}{a}$$ is positive. So $$a - \frac{1}{a} = 7$$.

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