Let a > 0, b > O, prove: ln (a + b) / 2 > = (LNA + LNB) / 2

(LNA + LNB) / 2 = (LN (a * b)) / 2 = ln (the square root of AB)
Because (a + b) / 2 > = the square root of ab
The monotone increasing function of LNX in its domain of definition
So ln (a + b) / 2 > = (LNA + LNB) / 2

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