Question

(x^2-x+2)^2-3(x^2-x+3)=1

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Let's solve the equation step-by-step:

1. Expand the terms: (x^2 - x + 2)^2 = (x^2 - x + 2) * (x^2 - x + 2) = x^4 - 2x^3 + 5x^2 - 2x + 4 -3(x^2 - x + 3) = -3x^2 + 3x - 9

2. Substitute the expanded terms back into the equation: (x^4 - 2x^3 + 5x^2 - 2x + 4) - (3x^2 - 3x + 9) = 1

3. Combine like terms: x^4 - 2x^3 + 5x^2 - 2x + 4 - 3x^2 + 3x - 9 = 1

4. Simplify the equation: x^4 - 2x^3 + 2x^2 + x - 5 = 1

5. Move all terms to one side to set the equation to zero: x^4 - 2x^3 + 2x^2 + x - 5 - 1 = 0

6. Combine constants: x^4 - 2x^3 + 2x^2 + x - 6 = 0

At this point, we have a fourth-degree polynomial equation. Solving this equation analytically for exact solutions can be quite complex. While it's possible to solve such equations using numerical methods or graphing calculators, there's no straightforward way to obtain a simple closed-form solution like we would with linear or quadratic equations.

Without more specific context or requirements for the solutions (e.g., a certain range, approximate values), I'm afraid I can't provide the exact solutions in this case. If you need specific numerical solutions, you can use numerical methods like Newton's method or use graphing tools to estimate the solutions.