Menu Close

Find-the-value-s-of-a-b-and-c-if-x-a-x-2020-1-x-b-x-c-where-a-b-and-c-are-natural-numbers-

Tinku Tara 0 Comments
Pin




Question Number 109029 by nimnim last updated on 20/Aug/20
Find the value(s) of a,b and c if: (x+a)(x+2020)+1=(x+b)(x+c) where a,b and c are natural numbers.
Findthevalue(s)ofa,bandcif:(x+a)(x+2020)+1=(x+b)(x+c)wherea,bandcarenaturalnumbers.
Answered by floor(10²Eta[1]) last updated on 21/Aug/20
x^2 +(2020+a)x+2020a+1=x^2 +(b+c)x+bc ⇒2020+a=b+c ⇒2020a+1=bc a=b+c−2020 2020(b+c−2020)+1=bc 2020b+2020c−2020^2 +1=bc bc−2020b−2020c+2020^2 =1 (b−2020)(c−2020)=1 the only ways we can factor 1 are 1.1 or (−1)(−1) I case: b−2020=1=c−2020 ⇒b=c=2021∴a=2022 II case: b−2020=−1=c−2020 ⇒b=c=2019∴a=2018 so all solutions a, b, c are: (2022, 2021, 2021), (2018, 2019, 2019)
x2+(2020+a)x+2020a+1=x2+(b+c)x+bc⇒2020+a=b+c⇒2020a+1=bca=b+c−20202020(b+c−2020)+1=bc2020b+2020c−20202+1=bcbc−2020b−2020c+20202=1(b−2020)(c−2020)=1theonlywayswecanfactor1are1.1or(−1)(−1)Icase:b−2020=1=c−2020⇒b=c=2021∴a=2022IIcase:b−2020=−1=c−2020⇒b=c=2019∴a=2018soallsolutionsa,b,care:(2022,2021,2021),(2018,2019,2019)
Commented by Rasheed.Sindhi last updated on 22/Aug/20
O_W ^W !_! ^! , great!...Thanks floor Sir!
OWW!!!,great!…ThanksfloorSir!

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *