Question:
Tick (✓) the correct answer:
If $\left(x-\frac{1}{x}\right)=6$, then $\left(x^{2}+\frac{1}{x^{2}}\right)=?$
(a) 36
(b) 38
(c) 32
(d) $36 \frac{1}{36}$
Solution:
(b) 38
$\left(x-\frac{1}{x}\right)=6$
$\Rightarrow$ Squaring both the sides:
$\Rightarrow\left(x-\frac{1}{x}\right)^{2}=(6)^{2}$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}-2(x)\left(\frac{1}{x}\right)\right)=36$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)-2=36$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)=36+2$
$\Rightarrow\left(x^{2}+\frac{1}{x^{2}}\right)=38$