Answer to Question #11038 in Algebra for nks prasad

Question

factorize
(x+1/x)^2+6(x+1/x)+9

Answer 1

Let's solve quadratic equation

y² + 6y + 9 = 0.

It's only solution is y = -3. So,

y² + 6y + 9 = (y+3)²

and

(x+1/x)²+6(x+1/x)+9 = (x+1/x+3)².