已知m,n∈R,f(x)=xˆ2-mnx.证明不等式f(mˆ2)+f(nˆ2)>=0

由f(x)=xˆ2-mnx则有f(mˆ2）=m^4-mnm^2=m^4-m^3n f(n^2)=n^4-mnn^2=n^4-mn^3f(mˆ2)+f(nˆ2)=m^4-m^3n +n^4-mn^3=m^3(m-n)+n^3(n-m)=(m-n)(m^3-n^3)=(m-n)(m-n)(m^2+mn+n^2)=(m-n)^2(m^2+mn+n^2) (...