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Question Number 152314 by mathdanisur last updated on 27/Aug/21

Answered by ghimisi last updated on 27/Aug/21

(a^2 /(a^2 +ab+b^2 ))+(c^2 /(c(a+b+c)))≥(((a+c)^2 )/(a^2 +b^2 +c^2 +ab+bc+ac)) (b^2 /(b^2 +cb+c^2 ))+(a^2 /(a(a+b+c)))≥(((a+b)^2 )/(a^2 +b^2 +c^2 +ab+bc+ac)) (c^2 /(c^2 +ac+a^2 ))+(b^2 /(b(a+b+c)))≥(((b+c)^2 )/(a^2 +b^2 +c^2 +ab+bc+ac))⇒ Σ(a^2 /(a^2 +ab+b^2 ))+1≥2⇒Σ(a^2 /(a^2 +ab+b^2 ))≥1

a2a2+ab+b2+c2c(a+b+c)⩾(a+c)2a2+b2+c2+ab+bc+acb2b2+cb+c2+a2a(a+b+c)⩾(a+b)2a2+b2+c2+ab+bc+acc2c2+ac+a2+b2b(a+b+c)⩾(b+c)2a2+b2+c2+ab+bc+ac⇒Σa2a2+ab+b2+1⩾2⇒Σa2a2+ab+b2⩾1

Commented by mathdanisur last updated on 27/Aug/21

Thank You Ser

ThankYouSer

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