Question

If $a^2+\frac{1}{a^2}=23$, find the value of $(a+\frac{1}{a})$

Answer 1

Given,

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

or, ${(a+\frac{1}{a})}^2-2.a.\frac{1}{a}=23$

or, ${(a+\frac{1}{a})}^2=23+2$

or, ${(a+\frac{1}{a})}^2=25$

or, $(a+\frac{1}{a})=\pm 5.$