若x^2-y^2=55,x-y=5,求(x+y)^ - 知识问答

若x^2-y^2=55,x-y=5,求(x+y)^2的值.

2个回答

∵x²-y²=(x+y)(x-y)=55,x-y=5
∴x+y=(x²-y²)÷(x-y)
=55÷5
=11
∴(x+y)²=11²=121
∵(a+b)²=a²+2ab+b²=7,(a-b)²=a²-2ab+b²=4
∴ab=[(a+b)²-(a-b)²]/4
=(7-4)/4
=3/4

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