Question

If $a+\frac{1}{a}=3;find=a^2+\frac{1}{a^2}$

Answer 1

If ${(a+\frac{1}{a})}^2=a^2+\frac{1}{a^2}+2\Rightarrow (3{)}^2=a^2+\frac{1}{a^2}+2\Rightarrow 9=a^2+\frac{1}{a^2}+2\Rightarrow 9-2=a^2+\frac{1}{a^2}\Rightarrow 7=a^2+\frac{1}{a^2}\therefore a^2+\frac{1}{a^2}=7$.