已知x≠y,x²-x=5,y²-y=5,求x+y+ - 知识问答

已知x≠y,x²-x=5,y²-y=5,求x+y+7的值

3个回答

∵x²-x=5,y²-y=0
∴(x²-x)-(y²-y)=0
x²-x-y²+y=0
(x²-y²)-(x-y)=0
(x+y)(x-y)-(x-y)=0
(x+y-1)(x-y)=0
∵x≠y
∴x-y≠0
∴x+y-1=0
即x+y=1
∴x+y+7
=(x+y)+7
=1+7
=8

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