Question

Expand ${(x+\frac{1}{x})}^2$ using appropriate identity

Answer 1

Using the identity: $(a+b{)}^2=a^2+b^2+2ab$.

Given:${(x+\frac{1}{x})}^2$ and apply the above identity by taking $a=x$ and $b=\frac{1}{x}$ in the given identity.

We get, ${(x+\frac{1}{x})}^2=x^2+{\left(\frac{1}{x}\right)}^2+(2\times x\times \frac{1}{x})=x^2+\frac{1}{x^2}+2$

Hence, ${(x+\frac{1}{x})}^2=x^2+2+\frac{1}{x^2}$.