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Question Number 141381 by loveineq last updated on 19/May/21
Let  a,b ≥ 0 . Prove that                   (a+b+2)^3  ≥ ((27)/2)(a^2 +ab+b^2 )
$$\mathrm{Let}\:\:{a},{b}\:\geqslant\:\mathrm{0}\:.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({a}+{b}+\mathrm{2}\right)^{\mathrm{3}} \:\geqslant\:\frac{\mathrm{27}}{\mathrm{2}}\left({a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} \right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

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