Question

Решите уравнение методом подстановки:

Answer 1

Объяснение:

$y = 2 + x \\ x {}^{3} - y {}^{3} = - 8 \\ \\ \\ x {}^{3} - (2 + x) {}^{3} = - 8 \\ x {}^{3} - 8 - 12x - 6x {}^{2} - x {}^{3} = - 8 \\ 6x {}^{2} + 12x + 8 = - 8 \\ 6x {}^{2} + 12x = 0 \\ x(6x + 12) = 0 \\ a) \: x 1= 0 \\ b) \: 6x + 12 = 0 \\ 6x = - 12 \\ x2 = - 2 \\ \\ y1 = 2 + 0 = 2 \\ y2 = 2 + ( - 2) = 0$

Ответ: x1=0 ; x2=-2; y1=2 ; y2=0

$x = 1 - 2y \\ 2x {}^{2} + 3xy - 3y {}^{2} = 6 \\ \\ 2(1 - 2y) {}^{2} + 3(1 - 2y)y - 3y {}^{2} = 6 \\ ... \\ y1 = - 1 \\ y2 = 4 \\ \\ x1 = 1 - 2( - 1) = 3 \\ x2 = 1 - 2 \times 4 = - 7$

Ответ: x1=3; y1=-1; x2=-7; y2=4