1.方程x^2y^2+9x^2+y^2-12xy=9的负整数解是?
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1.方程x^2y^2+9x^2+y^2-12xy=9的负整数解是?
1.方程x^2y^2+9x^2+y^2-12xy=9的负整数解是?
1.方程x^2y^2+9x^2+y^2-12xy=9的负整数解是?
x^2*y^2+9x^2+y^2-12xy=9
(x^2*y^2-6xy)+(9x^2+y^2-6xy)=9
(x^2*y^2-6xy+9)+(9x^2+y^2-6xy)=9+9
(xy-3)^2+(3x-y)^2=18
因为x,y是非负整数,所以(xy-3)^2的值(3x-y)^2的值只能在0,1,4,9,16中选
那么只有9+9=18
所以(xy-3)^2=9,(3x-y)^2=9
解之,得x1=1,y1=0;x2=0,y2=3;x3=2,y3=3;x4=1,y4=6
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