Question

Решите уравнение 1) 5x^3 - 5х = 0;
2) 64x^3 - 16х^2 +х= 0;
3) X^3-3x^2 - 4x + 12 = 0.
Докажите, что значение выражения 4^6— 7^3 делится на цело на 9

Answer 1

$1)5x {}^{3} - 5x = 0 \\ 5x(x {}^{2} - 1) = 0 \\ x(x {}^{2} - 1) = 0 \\ x1 = 0 \\ x2 = 1 \\ x3 = - 1$

$64x {}^{3} - 16x {}^{2} + x = 0 \\ x(64x {}^{2} - 16x + 1) = 0 \\ x(8x - 1) {}^{2} = 0 \\ x1 = 0 \\ x2 = \frac{1}{8}$

$x {}^{3} - 3x {}^{2} - 4x + 12 = 0 \\ x {}^{2} (x - 3) - 4(x - 3) = 0 \\ (x - 3)(x {}^{2} - 4) = 0 \\ x1 = 3 \\ x2 = 2 \\ x3 = - 2$