化简求值:已知x、y满足:x2+y2-4x+6y+13=0,求代数式(3x+y)2-3(3x-y)(x+y)-(x-3y)(x+3y)的值.
问题描述:
化简求值:已知x、y满足:x2+y2-4x+6y+13=0,求代数式(3x+y)2-3(3x-y)(x+y)-(x-3y)(x+3y)的值.
答
原式=9x2+6xy+y2-3(3x2+3xy-xy-y2)-(x2-9y2)
=9x2+6xy+y2-9x2-6xy+3y2-x2+9y2
=-x2+13y2
∵x2+y2-4x+6y+13=0,
∴(x-2)2+(y+3)2=0,
∴x=2,y=-3,
当x=2,y=-3时,原式=-4+13×9=113.