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)^_数学解答

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

人气：239 ℃　时间：2019-12-23 06:15:21

解答

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=0x=1/2y=1/2x+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)^...