let-a-b-c-x-y-and-z-be-complex-number-such-that-a-b-c-x-2-b-c-a-y-2-c-a-b-z-2-xy-yz-zx-1000-and-x-y-z-2016-find-the-value-of-xyz- Tinku Tara June 4, 2023 Algebra 0 Comments FacebookTweetPin Question Number 25066 by Mr easy last updated on 02/Dec/17 leta,b,c,x,yandzbecomplexnumbersuchthata=b+cx−2,b=c+ay−2c=a+bz−2.xy+yz+zx=1000andx+y+z=2016findthevalueofxyz. Answered by ajfour last updated on 03/Dec/17 Π(x−2)=xyz−2Σxy+4Σx−8(a+b)(b+c)(c+a)abc=xyz−2000+8064−8⇒xyz=(a+b)(b+c)(c+a)abc−6056Further,x+y+z=8+Σ(b+ca)=2016…(i)Σ(x−2)(y−2)=Σ(b+ca)(c+ab)Σxy−2Σ(x+y)+12=Σ(b+ca)(c+ab)1000−4×2016+12=Σ(b+ca)(c+ab)⇒Σ(b+ca)(c+ab)=7056sob+ca,c+ab,a+bcarerootsofcubicequation:q3−2008q2+7056q−(xyz+6056)=0….maycontinue.. Commented by jota+ last updated on 03/Dec/17 Theendisxyz=(a+b)(b+c)(c+a)abc−6056. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: la-valeur-de-l-integrale-1-o-x-x-Next Next post: Question-156137 Leave a Reply Cancel replyYour email address will not be published.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.