Question

已知(x-1/2)平方+|y-1|=0,求2x平方y-2xy+x平方y-xy的值

Answer 1

(x-1/2)平方+|y-1|=0,
x=1/2 y=1
x平方y-2xy+x平方y-xy
=xy(x-2y)+xy(x-1)
=xy(2x-2y-1)
=1/2(1-2-1)
=-1

Answer 2

（x-1/2)平方+|y-1|=0,x=1/2,y=1
2x^2*y-2xy+x^2*y-xy=2xy(x-1)+xy(x-1)=(x-1)*3xy
把x=1/2,y=1带入上式中，得(x-1)*3xy=(1/2-1)*3*1/2*1=3/4

Answer 3

因为(x-1/2)平方>=0,|y-1>|=0
只有：x-1/2=0,y-1=0
x=1/2,y=1
2x平方y-2xy+x平方y-xy
=3y(x^2-x)
=-3/4

Answer 4

(x-1/2)²+|y-1|=0
因为(x-1/2)²≥0，|y-1|≥0，要使等式成立，则(x-1/2)²=0，|y-1|=0
即x-1/2=0，y-1=0 得，x=1/2，y=1
2x²y-2xy+x²y-xy
=xy（2x-2+x-1）
=xy（3x-3）
=3xy（x-1）=3×1/2×1×（1/2-1）=3/2×（-1/2）=-3/4