4x2+9y2=(2x+3y)2+______=(2x-3y)2+______.
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4x2+9y2=(2x+3y)2+______=(2x-3y)2+______.
![4x2+9y2=(2x+3y)2+______=(2x-3y)2+______.](/uploads/image/z/15724594-10-4.jpg?t=4x2%2B9y2%3D%EF%BC%882x%2B3y%EF%BC%892%2B______%3D%EF%BC%882x-3y%EF%BC%892%2B______%EF%BC%8E)
∵(2x+3y)2=4x2+9y2+12xy,
∴4x2+9y2=(2x+3y)2-12xy,
∵(2x-3y)2=4x2+9y2-12xy,
∴4x2+9y2=(2x+3y)2+12xy.
∴4x2+9y2=(2x+3y)2-12xy,
∵(2x-3y)2=4x2+9y2-12xy,
∴4x2+9y2=(2x+3y)2+12xy.
已知x2+4x+y2-2y+5=0,则x2+y2=______.
若实数x,y满足3x2+2y2=6x,则x2+y2的最大值为______.
已知x+y=4,xy=2,则x2+y2+3xy=______.
分解因式(x+y)2+4(x-y)2-4(x2-y2)=______.
在有理数范围内分解因式:(x+y)4+(x2-y2)2+(x-y)4=______.
已知x+y=4,x2+y2=10,则(x-y)2=______.
已知xy=3,x2+xy-2y2=2(x+2y),且x≠-2y,则x+y=______.
已知x2-4y2=20,x+2y=5,则x=______,y=______.
已知x-y=2,则x2-y2-4y=______.
分解因式2x2-xy-6y2+7x+7y+3=______.
分解因式:x2-y2+3x-y+2=______.
(选做题)已知x+2y=1,则x2+y2的最小值是______.