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Question 6

If $$7a + \frac{1}{a} = \sqrt{90}$$, then the numerical value of $$a^3 + \frac{1}{a^3}$$ is

Solution

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TO BE FILLED - the printed condition must be checked against the paper, since as printed it does not lead to any of the four options. If the condition is $$a + \frac{1}{a} = \sqrt{2}$$, then $$a^3 + \frac{1}{a^3} = \left(a + \frac{1}{a}\right)^3 - 3\left(a + \frac{1}{a}\right) = 2\sqrt{2} - 3\sqrt{2} = -\sqrt{2}$$.

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