Question

If (x + 1/x) = 3, find the value of x² + 1/x².​

Answer 1

( x + 1/x )² = (3)²

a = x

b = 1/x

Identity used : ( a+b )² = a² + 2ab + b²

( x + 1/x )² = x² + 2*x*1/x = 1/x² — (3)² = 9

= x² + 2 + 1/x² = 9

x² + 1/x² = 9 - 2

x² + 1/x² = 7

Hence, The Answer is x² + 1/x² = 7.