Question

Factorize: (x² + 1/x²) - 4 ( x + 1/x ) + 6

Answer 1

Given : (x² + 1/x²) - 4 ( x + 1/x ) + 6

= x² + 1/x² – 4 ( x + 1/x ) + 4 + 2

By rearranging the terms :

= x² + 1/x² + 2 – 4 ( x + 1/x ) + 4

= x² + 1/x² + 2x × (1/x) – 4 ( x + 1/x ) + 4

= (x + 1/x)² – 4 (x + 1/x ) + 4

= (x + 1/x)² – 4 (x + 1/x ) + 2²

By Using Identity : a² + b² - 2ab = (a - b)²  

= {(x + 1/x) - 2}²

(x² + 1/x²) - 4 ( x + 1/x ) + 6 = {(x + 1/x) - 2}²

Hence (x² + 1/x²) - 4 ( x + 1/x ) + 6 is  {(x + 1/x) - 2}².

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Step-by-step explanation:

x^2+1/x^2=(x+1/x)^2 -2,

(x^2+1/x^2)-4(x+1/x)+6,

=(x+1/x)^2 -2-4(x+1/x)+6,

=(x+1/x)^2-2×2×(x+1/x)+2^2,

=(x+1/x -2)^2