x-y=9,xy=8.x^2+y^2＝?

x-y=9,xy=8.x^2+y^2＝?
x-y=9,xy=8.x^2+y^2＝?

x-y=9,xy=8.x^2+y^2＝?
x-y=9
===>(x-y)^2=81
===>x^2-2xy+y^2=81
xy=8
===>2xy=16
===>x^2+y^2=81+2xy=81+16=97

x^2+y^2=(x-y)^2+2xy=9^2+2*8=97

x^2+y^2=(x-y)^2+2xy=9^2+16=97.

x^2+y^2=x^2+y^2-2xy+2xy
=(x-y)^2+2xy
=9^2+2*8
=81+16
=97

x^2+y^2
=x^2-2xy+y^2+2xy
=(x-y)^2+2xy
=9^2+2*8
=81+16
=97

关键至于化为可以直接利用已知条件。