Question

Розвязати систему рівнянь x²+y²+2xy=4; x-y=4.​

Answer 1

Ответ:

$x {}^{2} + y { }^{2} + 2xy = 4 \\( x + y) {}^{2} = 4 \\ x - y = 4 \\ x = 4 + y \\ (4 + y + y) {}^{2} = 4 \\ (4 + 2y) {}^{2} = 4 \\16 + 16y + 4y {}^{2} - 4 = 0 \\ 4y {}^{2} + 16y + 12 = 0 \\ y {}^{2} + 4y + 3 = 0 \\ y1 = - 1 \\ y2 = - 3 \\ x1 = 4 + ( - 1) = 3 \\ x2 = 4 + ( - 3) = 1 \\ (3. - 1)(1. - 3)$