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) $36\frac{1}{36}$

Answer 1

(b) 38

$$\begin{gathered} \left(x-\frac{1}{x}\right)=6 \\ \Rightarrow Squaringboththesides: \\ \Rightarrow {\left(x-\frac{1}{x}\right)}^2={\left(6\right)}^2 \\ \Rightarrow \left(x^2+\frac{1}{x^2}-2\left(x\right)\left(\frac{1}{x}\right)\right)=36 \\ \Rightarrow \left(x^2+\frac{1}{x^2}\right)-2=36 \\ \Rightarrow \left(x^2+\frac{1}{x^2}\right)=36+2 \\ \Rightarrow \left(x^2+\frac{1}{x^2}\right)=38 \end{gathered}$$