r,s,t 是方程 8x^3+1001x+2008=0 的三个根。求 (r+s)^3+(s+t)^3+(r+t)^3 的值

Lucyding

r,s,t是等式8x^3+1001x+2008=0的根。求(r+s)^3+(s+t)^3+(r+t)^3的值

luyuanhong

fungarwai

\(r+s+t=0\)

\((r+s)^3+(s+t)^3+(r+t)^3
=-(r^3+s^3+t^3)\)
\(=\dfrac{1001(r+s+t)+3\times 2008}{8}=753\)