X²+XY+Y²=37 X²+XY+Y²=37
X³-Y³=37 (X-Y) (X²+XY+Y²) =37 ⇔ (X-Y)=1 ⇒X=1+Y
(1+Y)²+(1+Y)Y+Y²=37 1+2Y+Y²+Y+Y²+Y²-37=0 3Y²+3Y-36=0 ⇒
Y²+Y-12=0
Y1= -4 Y2=3
X1= -3 X2=4
ПРОВЕРКА
(-3;-4)
(-3)²+(-3)(-4)+(-4)²=9+12+16=37
(-3)³-(-4)³=- 27+64=37 ВЕРНО
(4;3)
(4)²+(4)(3)+(3)²=16+12+19=37
(4)³-(3)³=64- 27=37 ВЕРНО
ОТВЕТ: X1= -3 Y1= -4
X2=4 Y2=3