Question 51

$$ If a + \frac{1}{a} = 1, $$ find the value of $$ a^{3} + \frac{1}{a^{3}} $$

Given, $$a + \frac{1}{a} = 1$$

Cubing on both sides we get,

$$a^{3} + \frac{1}{a^{3}} + 3(a + \frac{1}{a}) = 1$$

$$ a^{3} + \frac{1}{a^{3}} = -2$$ ( as we know $$a + \frac{1}{a} = 1$$)

Hence, option B is the correct answer.

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