证明:a,b,c为正实数,令a^2=b^2=c^2,则:a^2=b^2=c^2=1/3a(1-a^2)=√(1/3)*(1-1/3)=(√3)/3 *2/3=(2√3)/9而当a^2=b^2=c^2时a(1-a^2)最大,故:a(1-a^2)<=(2√3)/9