a-b-c-N-such-that-a-3-b-b-3-c-Q-show-that-a-2-b-2-c-2-a-b-c-Z- Tinku Tara June 4, 2023 Number Theory 0 Comments FacebookTweetPin Question Number 113187 by bobhans last updated on 11/Sep/20 a,b,c∈Nsuchthata3+bb3+c∈Q,showthata2+b2+c2a+b+c∈Z Answered by bemath last updated on 11/Sep/20 Fact:3∉Q,p+q3∈Qifq=0considera3+bb3+c∈Q⇒(a3+b)(b3−c)3b−c=3ab−bc+3(b2−ac)3b−c∈Qitshouldbe:b2−ac=0orb2=acnowwehavea2+b2+c2a+b+c=(a+b+c)2−2(ab+ac+bc)a+b+c=(a+b+c)2−2(ab+b2+bc)a+b+c=(a+b+c)2−2b(a+b+c)a+b+c=(a+b+c)−2b=a−b+c∈Z(proved) Commented by Aina Samuel Temidayo last updated on 12/Sep/20 Butb2⩾2ac,youonlyconsideredb2=2ac Commented by bobhans last updated on 13/Sep/20 youarewrong Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: lim-x-0-3tan-4x-4tan-3x-3sin-4x-4sin-3x-Next Next post: calculate-A-n-0-1-sin-nx-e-2x-dx-with-n-integr-natural- Leave a Reply Cancel replyYour email address will not be published.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.