Question

(x2+x+1)2-8x2-8x-1=0​

Answer 1

Объяснение:

(х2+х+1)2-8х2-8х-1=0

4х+2х+2-16х-8х-1=0

4х+2х-16х-8х=-2+1+0

-18х=-1

х=18

Answer 2

To solve the equation (x^2 + x + 1)^2 - 8x^2 - 8x - 1 = 0, you can follow these steps:

1. Expand the square of the binomial (x^2 + x + 1)^2: (x^2 + x + 1)^2 = (x^2 + x + 1)(x^2 + x + 1) = x^4 + 2x^3 + 3x^2 + 2x + 1

2. Now, rewrite the equation with the expanded expression: (x^4 + 2x^3 + 3x^2 + 2x + 1) - 8x^2 - 8x - 1 = 0

3. Simplify the equation by combining like terms: x^4 + 2x^3 + 3x^2 + 2x + 1 - 8x^2 - 8x - 1 = 0

4. Combine like terms and simplify further: x^4 + 2x^3 - 5x^2 - 6x = 0

5. Factor out common terms: x(x^3 + 2x^2 - 5x - 6) = 0

6. Now, we need to solve the cubic polynomial x^3 + 2x^2 - 5x - 6. You can use numerical methods, a graphing calculator, or a computer algebra system to find the roots of this polynomial.

The solutions to the original equation are the roots of the cubic polynomial, plus x = 0 (from the factored term). You can use numerical methods or a calculator to find approximate values for the roots.