已知x+y=4,xy=1,求出x²-y²+8y的值
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已知x+y=4,xy=1,求出x²-y²+8y的值
已知x+y=4,xy=1,求出x²-y²+8y的值
已知x+y=4,xy=1,求出x²-y²+8y的值
你好
x+y=4
y-4=x
x²-y²+8y
=x²-(y²-8y+16)+16
=x²-(y-4)²+16
=x²-x²+16
=16
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所求式可化为:(x+y)(x-y)+8y=4x(x-y)+8y=4x-4y+8y=4x+4y=4x(x+y)=16
由x+y=4得 x=4-y x²-y²+8y= (4-y)²-y²+8y=16-8y+y²-y²+8y=16