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Question Number 155272 by bekzodjumayev last updated on 28/Sep/21

Commented by bekzodjumayev last updated on 28/Sep/21

$$\mathit{P}rovethat$$$$Pleasehelp$$

Commented by puissant last updated on 28/Sep/21

$$alna+blnb+clnc$$$$⩾(a+b+c)ln\left(\frac{a+b+c}{3}\right)$$$$⩾\frac{a+b+c}{3}[lna+lnb+lnc]$$$$⩾\frac{a+b+c}{3}\left[ln\left(abc\right)\right]$$$$\Rightarrow ln\left(a^a{b}^b{c}^c\right)⩾ln\left[{\left(abc\right)}^{\frac{a+b+c}{3}}\right]$$$$$$$$\Rightarrow a^a{b}^b{c}^c⩾{\left(abc\right)}^{\frac{a+b+c}{3}}...$$

Commented by bekzodjumayev last updated on 28/Sep/21

$$Thankyou$$

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