若xy为有理数,且x^2+y^2+1/2=x+y,求x+y因式分解:(m^2+2m)^2-(2m+4n^2)^2144(a-b)^2-225(a+b)^2

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若xy为有理数,且x^2+y^2+1/2=x+y,求x+y因式分解:(m^2+2m)^2-(2m+4n^2)^2144(a-b)^2-225(a+b)^2若xy为有理数,且x^2+y^2+1/2=x+

若xy为有理数,且x^2+y^2+1/2=x+y,求x+y因式分解:(m^2+2m)^2-(2m+4n^2)^2144(a-b)^2-225(a+b)^2
若xy为有理数,且x^2+y^2+1/2=x+y,求x+y
因式分解:
(m^2+2m)^2-(2m+4n^2)^2
144(a-b)^2-225(a+b)^2

若xy为有理数,且x^2+y^2+1/2=x+y,求x+y因式分解:(m^2+2m)^2-(2m+4n^2)^2144(a-b)^2-225(a+b)^2
x^2+y^2-x-y+1/4+1/4=0
(x^2-x+1/4)+(y^2-y+1/4)=0
(x-1/2)^2+(y-1/2)^2=0
x=1/2
y=1/2
x+y=1/2+1/2=1
(m^2+2m)^2-(4m+4n^2)^2
=[(m^2+2m)+(4m+4n^2)][(m^2+2m)-(4m+4n^2)]
=(m^2+6m+4n^2)(m^2-2m-4n^2)
144(a-b)^2-225(a+b)^2
=[12(a-b)+15(a+b)][12(a-b)-15(a+b)]
=(12a-12b+15a+15b)(12a-12b-15a-15b)
=-(27a+3b)(3a+27b)
=-9(9a+b)(a+9b)