Question

If $x^{3/2}+x^{-3/2}=3$, then the value of $x^6+\frac{1}{x^6}$ is

• A. 41
• B. 24
• C. 47
• D. 7

Answer 1

The correct option is C 47

$x^{3/2}+x^{-3/2}=3$
$\Rightarrow (x^{3/2}+\frac{1}{x^{3/2}}{)}^2=(3{)}^2$ $[a^{-x}=\frac{1}{a^x}]$
$\Rightarrow x^3+\frac{1}{x^3}+2=9$
$\Rightarrow (x^3+\frac{1}{x^3}{)}^2=(7{)}^2$
$\Rightarrow (x^3{)}^2+(\frac{1}{x^3}{)}^2+2\times x^3\times \frac{1}{x^3}=49$
$\Rightarrow x^6+\frac{1}{x^6}+2=49$
$\therefore x^6+\frac{1}{x^6}=47$
So, the correct answer is option (c).