设A=2x2-3xy+y2+x-3y,B=4x2-6xy+2y2+4x-y,若|x-3a|+(y+3)2=0,且B-2A
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设A=2x2-3xy+y2+x-3y,B=4x2-6xy+2y2+4x-y,若|x-3a|+(y+3)2=0,且B-2A=a.求A的值.
∵A=2x2-3xy+y2+x-3y,B=4x2-6xy+2y2+4x-y,
∴a=B-2A=(4x2-6xy+2y2+4x-y)-2(2x2-3xy+y2+x-3y)=4x2-6xy+2y2+4x-y-4x2+6xy-2y2-2x+6y=2x+5y,
∵|x-3a|+(y+3)2=0,
∴x-3a=0,y+3=0,即x=3a,y=-3,
则a=6a-15,即a=3,x=9,y=-3,
此时A=162+81+9+9+9=270.
∴a=B-2A=(4x2-6xy+2y2+4x-y)-2(2x2-3xy+y2+x-3y)=4x2-6xy+2y2+4x-y-4x2+6xy-2y2-2x+6y=2x+5y,
∵|x-3a|+(y+3)2=0,
∴x-3a=0,y+3=0,即x=3a,y=-3,
则a=6a-15,即a=3,x=9,y=-3,
此时A=162+81+9+9+9=270.
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