求最小值f(x)=x+1/(54x^2)(x>0)的最小值

Question

求最小值
f(x)=x+1/(54x^2)(x>0)的最小值

Answer 1

f(x)=x+1/(54x^2)=x/2+x/2+1/(54x^2)>=3*（x/2*x/2*1/54*1/x^2）^1/3 3*1/6=1/2
当x/2=1/(54x^2),"取等"
解得x=1/3
(利用3项和的均值不等式求),不知道你是否明白?例如a^3+b^3+c^3>=3abc(当a=b=c"取等")