284. г) x^2+x^3=0 д) 1-x^3=0 е) 1+x^3=0 з) 125-x^3=0 285. а) x^3+5x^2+6x=0 в) x^4=2x^3+3x^2 д) x^3-4x^2=x ж) x^5+x^3=x^4

г) x² + x³ = 0;

x² • (1 + x) = 0;

x² = 0;

1 + x = 0;

x = 0;

x = - 1.

д) 1 - x³ = 0;

- x³ = - 1;

x³ = 1;

x = 1.

е) 1 + x³ = 0;

x³ = - 1;

x = - 1.

з) 125 - x³ = 0;

- x³ = - 125;

x³ = 125;

x³ = 5³;

x = 5.

а) x³ + 5x² + 6x = 0;

x • (x² + 5x + 6) = 0;

x • (x² + 3x + 2x + 6) = 0;

x • (x • (x + 3) + 2 (x + 3)) = 0;

x • (x + 3) • (x + 2) = 0;

x = 0;

x + 3 = 0;

x + 2 = 0;

x = 0;

x = - 3;

x = - 2.

в) x⁴ = 2x³ + 3x²;

x⁴ - 2x³ - 3x² = 0;

x² • (x² - 2x - 3) = 0;

x² • (x • (x + 1) - 3 (x + 1)) = 0;

x² • (x + 1) • (x - 3) = 0;

x² = 0;

x + 1 = 0;

x - 3 = 0;

x = 0;

x = - 1;

x = 3.

д) x³ - 4x² = x;

x² - 4x² - x = 0;

x • (x² - 4x - 1) = 0;

x = 0;

x² - 4x - 1 = 0;

x = 0;

x = 2 + (√5);

x = 2 - (√5).

ж) x5 + x³ = x⁴;

x5 - x³ - x⁴ = 0;

x³ • (x² + 1 - x) = 0;

x³ = 0;

x² + 1 - x = 0;

x = 0.