-x %2B x^3 - 4*x^2 %2B 1=(x %2B 2)^3

1.	-x %2B x^3 - 4*x^2 %2B 1=(x %2B 2)^3
Answer» x3– 4x2– x + 1 = (x – 2)3 We have: x3– 4x2– x + 1 = (x – 2)3 ⇒ x3– 4x2– x + 1 = x3+ 3x2(– 2) + 3x(– 2)2+ (– 2)3 ⇒ x3– 4x2– x + 1 = x3– 6x2+ 12x – 8 ⇒ x3– 4x2– x – 1 – x3+ 6x2– 12x + 8 = 0 2x2– 13x + 9 = 0 Since 2x2– 13x + 9 is a quadratic polynomial ∴ x3– 4x2– x + 1 = (x – 2)3is a quadratic equation.

Answer»

x3– 4x2– x + 1 = (x – 2)3

We have:

x3– 4x2– x + 1 = (x – 2)3

⇒ x3– 4x2– x + 1 = x3+ 3x2(– 2) + 3x(– 2)2+ (– 2)3

⇒ x3– 4x2– x + 1 = x3– 6x2+ 12x – 8

⇒ x3– 4x2– x – 1 – x3+ 6x2– 12x + 8 = 0

2x2– 13x + 9 = 0

Since 2x2– 13x + 9 is a quadratic polynomial

∴ x3– 4x2– x + 1 = (x – 2)3is a quadratic equation.

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