Question

解方程组x²-2xy+y²=1 2x²-5xy-3y²=0

Answer 1

x²-2xy+y²=1

2x²-5xy-3y²=0

即

(x-y)²=1

(2x+y)(x-3y)=0

2x+y=0或x-3y=0

如果2x+y=0,则y=-2x

带入(x-y)²=1有(3x)²=1,3x=±1,x=±1/3；此时x=1/3,y=-2/3或x=-1/3,y=2/3

如果x-3y=0,则x=3y

带入(x-y)²=1有(2y)²=1,2y=±1,y=±1/2；此时x=3/2,y=1/2或x=-3/2,y=-1/2