x+y=10,xy=24 x^2-xy+y^2=??? 救命!!!

x^2-xy+y^2
=(x^2+2xy+y^2)-3xy
=(x+y)^2-3xy
=10^2-3*24
=100-72
=28

x+y=10 (1)
xy=24 (2)
可求得x=4,y=6或者x=6,y=4

将以上结果代入所求式子得28

(x+y)^=x^2+2xy+y^2=100
x^2+y^2=52
x^2-xy+y^=28

原式=(x+y)^2-3xy=100-72=28

x^2-xy+y^2=(x+y)^2-3xy=10*10-3*24=28

x^2-xy+y^2
=(x+y)^2-2xy-xy
因为x+y=10，xy=24
所以x^2-xy+y^2=10^2-48-24=28