Question 6

# $$If a^{2} + \frac{1}{a^{2}} = 3, then a^{3} + \frac{1}{a^{3}}$$ = ?

Solution

The correct option is B.

Given $$a^{2}$$ + $$\frac{1}{a^{2}}$$ = 3

$$(a+\frac{1}{a})$$ $$^{2}$$ = $$a^{2}+\frac{1}{a^{2}}$$ + 2

$$\Rightarrow$$ $$(a+\frac{1}{a})$$ = $$\sqrt(3+2)$$ = $$\sqrt5$$

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

$$\Rightarrow$$ ($$\sqrt5$$)$$^{3}$$ = $$a^{3}+\frac{1}{a^{3}}$$ + 3($$\sqrt5$$)

$$\Rightarrow$$ $$a^{3}+\frac{1}{a^{3}}$$ = $$5\sqrt5-3\sqrt5=2\sqrt5$$