Question

If $a^2+\frac{1}{a^2}=23;finda+\frac{1}{a}$

Answer 1

${(a+\frac{1}{a})}^2=a^2+\frac{1}{a^2}+2\Rightarrow {(a+\frac{1}{a})}^2=23+2\Rightarrow {(a+\frac{1}{a})}^2=25\Rightarrow a+\frac{1}{a}=\sqrt{25}\Rightarrow a+\frac{1}{a}=5$.