Question

If the value of (a+1/a) is equal to 3,then what will be the value of a2+1/a2?

Answer 1

Given, $\left(a+\frac{1}{a}\right)=3$

we know, (A + B)² = A² + B² + 2AB

if we assume , A = a and B = 1/a
then,
$\left(a+\frac{1}{a}\right)^2=a^2+\frac{1}{a^2}+2a\frac{1}{a}\\\\\\(3)^2=a^2+\frac{1}{a^2}+2\\\\\\9=a^2+\frac{1}{a^2}+2\\\\\\9-2=7=a^2+\frac{1}{a^2}$

hence, a² + 1/a² = 7