Question

решите СИСТЕМУ уравнений
х+у=-2
х^2+y^2=100

Answer 1

Y = - X - 2 ; Y^2 = - X^2 - 4XY - 4 ; X^2 - X^2 - 4XY - 4 - 100 = 0 ; 4X * ( - X - 2 ) + 104 = 0 ; - 4X^2 - 8X + 104 = 0 ; X^2 + 2X - 26 = 0 ; D = 4 + 104 = 108 ; V D = V 108 = V ( 36 * 3 ) = 6 V 3 ; X1 = ( - 2 + 6 V 3 ) : 2 = - 1 + 3 V 3 ; X2 = - 1 - 3 V 3 ; Y = - X - 2 ; Y1 = 1 - 3 V 3 - 2 = - 1 - 3 V 3 ; Y2 = 1 + 3 V 3 - 2 = - 1 + 3 V 3

Answer 2

х+у=-2
х²+y²=100

x=-2-y
(-2-y)²+y²=100
y²+4y+4+y²-100=0
2y²+4y-96=0
Разделим все на 2
y²+2y-48=0
D=4+192=196=14²
y1=(-2+14)/2=6
y2(-2-14)/2=-8

x=-2-y
x1=-2-y1=-2-6=-8
x2=-2-y2=-2+8=6

Ответ: (-8 ; 6) и ( 6 ; -8)