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a-b-gt-0-2a-b-1-prove-that-a-2-b-2-2a-2a-b-2-gt-2-




Question Number 208513 by CrispyXYZ last updated on 17/Jun/24
a, b>0. 2a+b=1, prove that  ((a^2 +b^2 )/(2a))+((2a)/b^2 ) > 2.
$${a},\:{b}>\mathrm{0}.\:\mathrm{2}{a}+{b}=\mathrm{1},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}{a}}+\frac{\mathrm{2}{a}}{{b}^{\mathrm{2}} }\:>\:\mathrm{2}. \\ $$

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