Question

Розв'яжіть рівняння:
1)3x(x2-9)=0
3)4x3-4x=0
5)2x3-7x2+6x=0
7)2x3-5x2+6x-15=0
Цифры после "x" - это квадраты/кубы

Answer 1

Ответ:

$1)3x(x {}^{2} - 9) = 0 \\ x(x { }^{2} - 9) = 0 \\ x = 0 \\ x {}^{2} - 9 = 0 \\ x1 = - 3 \\ x2 = 0 \\ x3 = 3$

$3)4x {}^{3} - 4x = 0 \\ 4x(x {}^{2} - 1) = 0 \\ x(x {}^{2} - 1) = 0 \\ x = 0 \\ x { }^{2} - 1 = 0 \\ x1 = - 1 \\ x2 = 0\\ x3 = 1$

$5)2x {}^{3} - 7x {}^{2} + 6x = 0 \\ x(2x {}^{2} - 7x + 6) = 0 \\ x(2x {}^{2} - 3x - 4x + 6) = 0 \\ x(x(2x - 3) - 2(2x - 3)) = 0 \\ x(2x - 3) \times (x - 2) = 0 \\ x = 0 \\ 2x - 3 = 0 \\ x - 2 = 0 \\ x1 = 0 \\ x2 = \frac{3}{2} \\ x3 = 2$

$7)2x {}^{3} - 5x {}^{2} + 6x - 15 = 0 \\ x {}^{2} (2x - 5) + 3(2x - 5) = 0 \\ (2x - 5)(x {}^{2} + 3) = 0 \\ 2x - 5 = 0 \\ x { }^{2} + 3 = 0 \\ x = \frac{5}{2}$