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Question Number 143979 by mathdanisur last updated on 20/Jun/21

Answered by mitica last updated on 20/Jun/21

p=x+y+z;q=xy+yz+xz;r=xyz⇒p^2 ≥3q 3(p+((3r)/q))^4 =3((p/3)+(p/3)+(p/3)+((3r)/q))^4 ≥^(am−gm) ≥3(4∙(((p/3)∙(p/3)∙(p/3)∙((3r)/q)))^(1/4) )^4 =3∙256∙((p^3 r)/(9q))=((256)/3)∙((pr)/q)∙p^2 ≥((256)/3)∙((pr)/q)∙3q=256pr

p=x+y+z;q=xy+yz+xz;r=xyz⇒p2⩾3q3(p+3rq)4=3(p3+p3+p3+3rq)4⩾am−gm⩾3(4⋅p3⋅p3⋅p3⋅3rq4)4=3⋅256⋅p3r9q=2563⋅prq⋅p2⩾2563⋅prq⋅3q=256pr

Commented by justtry last updated on 20/Jun/21

it′s great..i to understanding, maybe you want write ((256)/(3 )).((pr)/q).p^2 (but is writen q^2 )

it′sgreat..itounderstanding,maybeyouwantwrite2563.prq.p2(butiswritenq2)

Commented by mitica last updated on 20/Jun/21

p^2

p2

Commented by mathdanisur last updated on 20/Jun/21

thnks sir, alot cool

thnkssir,alotcool

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