先化简,在求值;2(x-y)^2+(x+y)(x-y),其中x^2+y^2-6x+2y+10=0

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 13:39:31
先化简,在求值;2(x-y)^2+(x+y)(x-y),其中x^2+y^2-6x+2y+10=0

先化简,在求值;2(x-y)^2+(x+y)(x-y),其中x^2+y^2-6x+2y+10=0
先化简,在求值;2(x-y)^2+(x+y)(x-y),其中x^2+y^2-6x+2y+10=0

先化简,在求值;2(x-y)^2+(x+y)(x-y),其中x^2+y^2-6x+2y+10=0
(x²-6x+9)+(y²+2y+1)=0
(x-3)²+(y+1)²=0
所以
x=3,y=-1
原式=2x²-4xy+2y²+x²-y²
=3x²-4xy+y²
=27+12+1
=40

x^2+y^2-6x+2y+10=0
(x-3)²+(y+1)²=0
x-3=0,y+1=0
x=3,y=-1
所以
2(x-y)^2+(x+y)(x-y)
=2x²-4xy+2y²+x²-y²
=3x²-4xy+y²
=3×3²-4×3×(-1)+1
=27+12+1
=40

x^2+y^2-6x+2y+10=0
(x-3)^2+(y+1)^2=0
x=3
y=-1

2(x-y)^2+(x+y)(x-y)
=(x-y)(2x-2y+x+y)
=(x-y)(3x-y)
=4*10
=40