解方程组 x3+y3=468 x2y+xy2=420

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解方程组x3+y3=468x2y+xy2=420解方程组x3+y3=468x2y+xy2=420解方程组x3+y3=468x2y+xy2=420记a=x+y,b=xyx^2y+xy^2=420,化为:

解方程组 x3+y3=468 x2y+xy2=420
解方程组 x3+y3=468 x2y+xy2=420

解方程组 x3+y3=468 x2y+xy2=420
记a=x+y,b=xy
x^2y+xy^2=420,化为:xy(x+y)=420,即ab=420
x^3+y^3=468,化为;(x+y)(x^2-xy+y^2)=468,即a(a^2-3b)=468,得：a^3-3ab=468,故a^3-3*420=468
得：a^3=1728
得：a=12
故b=420/a=35
因此x,y为方程t^2-12t+35=0的两根
（t-5)(t-7)=0
t=5,7
故原方程有两组(5,7)及(7,5)

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