[Toán 9] Tìm max $a+b$

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doremon707

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noinhobinhyen

Ta có $2=a^3+b^3=(a+b)^3 - 3ab.(a+b) \geq (a+b)^3-3.\dfrac{(a+b)^2}{4}.(a+b)$

$\Leftrightarrow \dfrac{(a+b)^3}{4} \leq 2$

$\Leftrightarrow a+b \leq 2$

Dấu [=] xảy ra khi a=b=1
 
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