作业帮已知x^2+xy=13,且xy+y2=12,求(x+y)(x-y)和（x+y）^2
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已知x^2+xy=13,且xy+y2=12,求(x+y)(x-y)和（x+y）^2
已知x^2+xy=13,且xy+y2=12,求(x+y)(x-y)和（x+y）^2
已知x^2+xy=13,且xy+y2=12,求(x+y)(x-y)和（x+y）^2
x^2+xy=13,且xy+y2=12
∴(x+y)(x-y)
=x²-y²
=x²+xy-xy-y²
=x²+xy-(xy+y²)
=13-12
=1
(x+y)²=x²+2xy+y²
=x²+xy+xy+y²
=13+12
=25
前式减后式得x^2-y^2=1,即(X+y)(x-y)=1
前式加后式得x^2+2xy+y^2=25,即(X+y)^2=25
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