Question

If $x=2+\sqrt{3}$ and $y=2-\sqrt{3}$; find the value of $x^{-3}+y^{-3}$

• A. 42
• B. 48
• C. 50
• D. 52

Answer 1

Answer: (D)

52

$x+y=4;xy=1$
$\Rightarrow x-3+y-3=\frac{1}{x^3}+\frac{1}{y^3}$
$\Rightarrow \frac{x^3+y^3}{{\left(xy\right)}^3}=\frac{{(x+y)}^3-3xy(x+y)}{{\left(xy\right)}^3}$
$=\frac{4^3-3\times 4}{1^3}=52$