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Question Number 141454 by loveineq last updated on 19/May/21

Let a,b,c ≥ 0 and a+b+c = 4. Prove that ((a^2 +ab+b^2 )/((a+b+4)^2 ))+((b^2 +bc+c^2 )/((b+c+4)^2 ))+((c^2 +ca+a^2 )/((c+a+4)^2 )) ≤ (1/2)

Leta,b,c⩾0anda+b+c=4.Provethata2+ab+b2(a+b+4)2+b2+bc+c2(b+c+4)2+c2+ca+a2(c+a+4)2⩽12

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