Question

初中方程竞赛题实数a,b,c满足a+b+c=9,a平方+b平方+c平方=29,a立方+b立方+c立方=99,则a=?b=

Answer 1

a+b=9-c

a^2+b^2=29-c^2

a^3+b^3=99-c^3

(a+b)^2=29-c^2+2ab=(9-c)^2

ab=[(9-c)^2-29+c^2]/2=c^2-9c+26;

a^3+b^3=(a+b)(a^2+b^2-ab)=(9-c)(29-c^2-ab)=(9-c)[29-c^2-(c^2-9c+26)]=99-c^3

(9-c)(3-2c^2+9c)=99-c^3

c^3-9c^2+26c-24=0

c=

明天继续