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Question Number 193750 by thean last updated on 19/Jun/23

	Answered by Subhi last updated on 19/Jun/23

	$o n l y o n e n u m b e r c a n b e z e r o t o g i v e t h e m i n i v a l u e$ $s u p p o s e b = 0 ⇛ a + c = 2$ $\frac{a}{3 a^{2}} + \frac{c}{3 c^{2}} = \frac{1}{3} (\frac{1}{a} + \frac{1}{b})$ $(a + b) (\frac{1}{a} + \frac{1}{b}) ⩾ {(1 + 1)}^{2} = 4 (c h a u c h y - s c h w a r t z)$ $(\frac{1}{a} + \frac{1}{b}) ⩾ \frac{4}{a + b} = \frac{4}{2} = 2$ $\frac{a}{3 a^{2}} + \frac{c}{3 c^{2}} = \frac{1}{3} (\frac{1}{a} + \frac{1}{b}) ⩾ \frac{2}{3}$
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