若x^2+xy+y^2=37,x^2-xy+y^2=13求x+y的值

问题描述:

若x^2+xy+y^2=37,x^2-xy+y^2=13求x+y的值

x^2+xy+y^2=37……①
x^2-xy+y^2=13……②
由①+②得:x^2+y^2=25
由①-②得:2xy=24
∵(x+y)^2=x^2+2xy+y^2=49
∴x+y=±7