如果(x+2y)^2-2(x+2y)(x-2y)+(x-2y)^2=16y且(2x-y)^2+2(2x-y)(2x+y)+(2x+y)^2=-16x求(x^y)^2003的值 x y都不等于0
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(x+2y)^2-2(x+2y)(x-2y)+(x-2y)^2=16y
[(x+2y)-(x-2y)]²=16y
16y²=16y
y²-y=0,
y(y-1)=0
y1=0,x y都不等于0,舍去;
y2-1=0,y2=1;
(2x-y)^2+2(2x-y)(2x+y)+(2x+y)^2=-16x
[(2x-y)+(2x+y)]²=-16x
16x²+16x=0
x(x+1)=0;
x1=0,x y都不等于0,舍去;
x2+1=0,x2=-1;
(x^y)^2003=[(-1)^1]^2003=(-1)^2003=-1;