Prove-that-a-b-b-c-c-a-a-2-1-b-2-1-b-2-1-c-2-1-c-2-1-a-2-1-for-a-b-c-are-positive-real-number- Tinku Tara June 4, 2023 Algebra 0 Comments FacebookTweetPin Question Number 150039 by bobhans last updated on 09/Aug/21 Provethatab+bc+ca⩾a2+1b2+1+b2+1c2+1+c2+1a2+1fora,b,carepositiverealnumber Answered by EDWIN88 last updated on 09/Aug/21 (∙)withCauchy−Schwarz′s(a2+b2)(a2+1)(b2+1)⩾(a2+b2)(ab+1)=ab(a2+b2)+a2+b2⩾ab(a2+b2+2)⇒Σab+Σba=Σa2+b2ab⩾Σa2+b2+2(a2+1)(b2+1)=Σa2+1b2+1+Σb2+1a2+1(∙)withChebyshev′sΣa2b2=Σa2b2+1+Σa2b2(b2+1)⩾Σa2b2+1+Σb2b2(b2+1)=Σa2+1b2+1then(1+Σab)2=1+2(Σab+Σba)+a2b2⩾1+2(Σa2+1b2+1+Σb2+1a2+1)+Σa2+1b2+1=(1+Σa2+1b2+1)2Thusab+bc+ca⩾a2+1b2+1+b2+1c2+1+c2+1a2+1 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Two-blocks-of-masses-M-and-2M-are-connected-to-each-other-through-a-light-spring-as-shown-in-figure-If-we-push-the-mass-M-with-a-force-F-which-cause-acceleration-a-in-mass-M-what-will-the-acceleratiNext Next post: Random-Problem-pi-4-pi-2-7sin-x-3cos-x-dx-By-getting-the-antiderivative-of-the-trigonometric-functions-sin-x-dx-cos-x-c-cos-x-dx-sin-x-c-7-sin-x-3-cos-x-pi-4- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.