解方程组 x3+y3=468 x2y+xy2=420

题目

解方程组 x3+y3=468 x2y+xy2=420

答案

记a=x+y,b=xyx^2y+xy^2=420,化为:xy(x+y)=420,即ab=420x^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...