Question

解方程组 x2+y2=10 x+xy+y=7

Answer 1

∵x^2+y^2=10,x+xy+y=7

∴ 7-xy=x+y,且2xy≤x^2+y^2=10,

∴(7-xy)^2=(x+y)^2=x^2+y^2+2xy=10+2xy,且xy≤5

∴49-14xy+(xy)^2=10+2xy,即(xy)^2-16xy+39=0,解得xy=3或xy=13(舍去)

∴x=3/y,代入x^2+y^2=10并整理得y^4-10y^2+9=0,解得y=1或y=-1或y=3或y=-3

∴当y=1时,x=3,当y=-1时,x=-3,当y=3时,x=1,当y=-3时,x=-1