Question

If $x=\frac{1}{4-\sqrt{15}},y=\frac{1}{4+\sqrt{15}}$, then value of $x^3+y^3$ is :

• A. $486$
• B. $439$
• C. $488$
• D. $476$

Answer 1

The correct option is C $488$

$x=\frac{1}{4-\sqrt{15}}=4+\sqrt{15}$

$y=\frac{1}{4+\sqrt{15}}=4-\sqrt{15}$

$x^3+y^3=(x+y)\left[\right(x+y{)}^2-3xy]$

$=8\left[\right(8{)}^2-3]$

$=488$

Hence, option $\left(3\right)$ is correct.