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(x-1)(x^2+x+1)-x(x+2)(x-2)=5

2 min read Jun 17, 2024
(x-1)(x^2+x+1)-x(x+2)(x-2)=5

Solving the Equation: (x-1)(x^2+x+1)-x(x+2)(x-2)=5

This article will guide you through the process of solving the equation (x-1)(x^2+x+1)-x(x+2)(x-2)=5.

Expanding and Simplifying

First, we need to expand and simplify the equation:

  1. Expand the first product: (x-1)(x^2+x+1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1

  2. Expand the second product: x(x+2)(x-2) = x(x^2 - 4) = x^3 - 4x

  3. Substitute the expanded expressions back into the original equation: x^3 - 1 - (x^3 - 4x) = 5

  4. Simplify: x^3 - 1 - x^3 + 4x = 5 4x - 1 = 5

Solving for x

  1. Isolate x: 4x = 6

  2. Divide both sides by 4: x = 6/4

  3. Simplify: x = 3/2

Solution

Therefore, the solution to the equation (x-1)(x^2+x+1)-x(x+2)(x-2)=5 is x = 3/2.

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