请尽快发来答案,要有过程,谢谢!!!!!!!!!!!
參考答案:这个是由余弦定理推导出来的
a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2)-a^3-b^3-c^3>2abc.
a(b^2+c^2-a^2)+b(c^2+a^2-b^2)+c(a^2+b^2-c^2)>2abc
2abccosA+2bcacosB+2abccosC>2abc
2abc(cosA+cosB+cosC)>2abc
cosA+cosB+cosC>1
cosA+cosB+cosC=cosA+cosB+cos(pi-(A+B))
=cosA+cosB-cos(A+B)
=2cos(A+B)/2*cos(A-B)/2+1-2cos^2(A+B)/2
=1+2cos(A+B)/2*(cos(A-B)/2-cos(A+B)/2)
=1+4cos(A+B)/2*(sinA/2+sinB/2)
=1+4sinA/2*sinB/2*sinC/2
sinA/2>0
sinB/2>0
sinC/2>0
4sinA/2*sinB/2*sinC/2>0
所以命题得证