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Question Number 143980 by mathdanisur last updated on 20/Jun/21

Answered by mitica last updated on 20/Jun/21

p=a+b+c;q=ab+bc+ac;r=abc⇒q^2 ≥3pr 3Σ(a/b)−Σ((3a+b+c)/(b+c))=3Σ((a/b)−(a/(b+c)))−3= 3Σ((ac)/(b(b+c)))−3=(3/(abc))Σ(((ac)^2 )/(b+c))−3≥ (3/r)∙(q^2 /(2p))−3≥((3∙3pr)/(2pr))−3=(3/2)>0⇒ 3((a/b)+(b/c)+(c/a))≥((3a+b+c)/(b+c))+((a+3b+c)/(a+c))+((a+b+3c)/(a+b))+(3/2)

p=a+b+c;q=ab+bc+ac;r=abc⇒q2⩾3pr3Σab−Σ3a+b+cb+c=3Σ(ab−ab+c)−3=3Σacb(b+c)−3=3abcΣ(ac)2b+c−3⩾3r⋅q22p−3⩾3⋅3pr2pr−3=32>0⇒3(ab+bc+ca)⩾3a+b+cb+c+a+3b+ca+c+a+b+3ca+b+32

Commented by mathdanisur last updated on 20/Jun/21

Cool sir thanks but p,q,r what it means?

Coolsirthanksbutp,q,rwhatitmeans?

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