Question

If $(1^3+2^3+3^3+4^3{)}^{3/2}=\frac{1}{x}$, then $x$ is

• A. $100$
• B. $\frac{1}{100}$
• C. $1000$
• D. $\frac{1}{1000}$

Answer 1

The correct option is D $\frac{1}{1000}$

$(1^3+2^3+3^3+4^3{)}^{3/2}=1$
$(1+8+27+64{)}^{3/2}=\frac{1}{x}$
$(100{)}^{3/2}=\frac{1}{x}$
$1000=\frac{1}{x}$
$\Rightarrow x=\frac{1}{1000}$