已知x+y=2,x+3y=5,求3x²+12xy+9y²的值

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已知x+y=2,x+3y=5,求3x²+12xy+9y²的值
已知x+y=2,x+3y=5,求3x²+12xy+9y²的值

已知x+y=2,x+3y=5,求3x²+12xy+9y²的值
3x²+12xy+9y²
=3(x²+4xy+3y²)
=3(x+y)(x+3y)
=3*2*5
=30

1、
(x+y)²=7²
x²+2xy+y²=49
xy=3
两边减去xy
x²+xy+y²=49-3=46
2、
(x-y)²
=x²-2xy+y²
=(x²+xy+y²)-3xy
=46-3×3
=37

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