高中不等式题1/(a^3)+1/(b^3)+1/(c^3)+abc大于等于 2√3
问题描述：
高中不等式题1/(a^3)+1/(b^3)+1/(c^3)+abc大于等于 2√3
答
因1/(a^3)+1/(b^3)+1/(c^3)≥3{[1/(a^3)]*[1/(b^3)]*[1/(c^3)]}^(1/3)=3[1/(a^3*b^3*c^3)]^(1/3)=3/(abc)所以1/(a^3)+1/(b^3)+1/(c^3)+abc≥3/(abc)+(abc)≥2{[3/(abc)]*(abc)}^(1/2)=2*3^(1/2)=2√3