Question

(x+10)*(x²-x+1)-x*(x-3)*(x-3)*(x+3)=-27

Answer 1

(x + 10)(x² - x + 1)  - x(x - 3)(x - 3)(x + 3) = -27

=> x(x² - x + 1) + 10(x² - x + 1) - x(x² - 9)(x - 3) = -27

=> x³ - x² + x + 10x² - 10x + 10 - x[x²(x - 3) - 9(x - 3)] = -27

=> x³ - x² + x + 10x² - 10x + 10 - x(x³ - 3x² - 9x + 27) = -27

=> x³ - x² + x + 10x² - 10x + 10 - x⁴ + 3x³ + 9x² - 27x = -27

=> (x³ + 3x³) + (-x² + 10x² + 9x²) + (x - 10x - 27x) + 10 - x⁴ = -27

=> 4x³ + 18x² - 36x + 10 - x⁴ = -27

=> -(x⁴ - 4x³ - 18x² + 36x - 10) = -27

=> vô nghiệm

Answer 2

\(\left(x+10\right)\left(x^2-x+1\right)-x\left(x-3\right)\left(x-3\right)\left(x+3\right)=-27\)

\(\Leftrightarrow x^3-x^2+x+10x^2-10x+10-x\left(x-3\right)^2\left(x+3\right)=-27\)

\(\Leftrightarrow x^3-11x^2-9x+10-x\left[\left(x^2-6x+9\right)\left(x+3\right)\right]=-27\)

\(\Leftrightarrow x^3-11x^2-9x+10-x\left(x^3+3x^2-6x^2-18x+9x+27\right)=-27\)

\(\Leftrightarrow x^3-11x^2-9x+10-x\left(x^3-3x^2-9x+27\right)=-27\)

\(\Leftrightarrow x^3-11x^2-9x+10-x^4+3x^3+9x^2-27x=-27\)

Vô nghiệm :) chắc rồi