решить систему уравнений x-y=6,x^2+y^2=20. Created by danilasolomko. algebra-ru

решить систему уравнений x-y=6,x^2+y^2=20...

StrangeStud X-y=6
x^2+y^2=20
1) x-y=6
x=6+y
2)x^2+y^2=20
(6+y)^2+y^2=20
36+12y+y^2+y^2=20
2y^2+12y+16=0
y^2+6y+8=0
y1=-4, y2 = -2
3) y = -4;
x=2
4) y = -2
x=4
Ответ: (2;-4),(4;-2)

2 votes Thanks 1

gregoriifdgdgf X=6+y
x²+y²=20⇒(6+y)²+y²=20⇒36+12y+y²+y²=20⇒2y²+12y+16=0⇒y²+6y+8=0, решая квадратное уравнение получим y1=-2; y2=-4⇒ при y=-2 x=4, при y=-4 x=2

1 votes Thanks 0

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