Question 58

If $$a^{3}+\frac{1}{a^{3}} = 52$$ then the value of $$2\left(a + \frac{1}{a}\right)$$ is :

Solution

$$a^{3}+\frac{1}{a^{3}} = 52$$

$$(a + \frac{1}{a})^3 - 3.a.\frac{1}{a}(a + \frac{1}{a}) = 52$$

$$(\because a^3 + b^3 = (a + b)^3 - 3ab(a + b))$$

$$(a + \frac{1}{a})^3 - 3(a + \frac{1}{a}) = 52$$

From the option A) -

Put the value of $$2(a + \frac{1}{a}) = 8$$,

$$(a + \frac{1}{a}) = 4$$

L.H.S.,

$$4^3 - 3 \times 4$$ = 52

= R.H.S.

$$\therefore$$ The value of $$2\left(a + \frac{1}{a}\right)$$ is 8.

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