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If-x-y-gt-0-then-prove-that-3-x-2-y-2-2-xy-2-x-y-




Question Number 137208 by bemath last updated on 31/Mar/21
If x,y > 0 then prove that    3(√((x^2 +y^2 )/2)) + (√(xy)) ≥ 2(x+y)
$$\mathrm{If}\:\mathrm{x},\mathrm{y}\:>\:\mathrm{0}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\:\mathrm{3}\sqrt{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\:+\:\sqrt{\mathrm{xy}}\:\geqslant\:\mathrm{2}\left(\mathrm{x}+\mathrm{y}\right)\: \\ $$

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