4. Let $x$ be a number such that $x+\frac{1}{x}=4$. Find the value of $x^{3}+\frac{1}{x^{3}}$.
(A) 48
(B) 50
(C) 52
(D) 54
(E) None of the above
4. Ans: C
$$
\begin{aligned}
x+\frac{1}{x}=4 & \Longrightarrow\left(x+\frac{1}{x}\right)^{3}=4^{3}=64 \\
& \Longrightarrow x^{3}+3 x+3 \cdot \frac{1}{x}+\frac{1}{x^{3}}=64 \\
& \Longrightarrow x^{3}+\frac{1}{x^{3}}+3\left(x+\frac{1}{x}\right)=64 \\
& \Longrightarrow x^{3}+\frac{1}{x^{3}}=64-3(4)=52 .
\end{aligned}
$$