Fewpal
+1 vote
242 views
in Mathematics by (7.5k points)
edited by

Find all integers a,b,c such that a2=bc+1 , b2=ac+1

1 Answer

+2 votes
by (13.5k points)
selected by
 
Best answer

Given : a2 = bc +  1                                                             ---- ( 1 )

And

b2 = ca + 1                                                                           ---- ( 2 )

Now we subtract equation 2 from equation 1 and get

a2 - b2 =  bc - ca

( a + b ) ( a - b ) = c ( b - a )

( a + b ) ( a - c )  = - c ( a - b )

( a + b ) = - c

c = - ( a + b )  , Substitute that value in equation 1 we get

a2  = b [ - ( a + b ) ] + 1

a2 = - ab - b2 + 1

a2 + ab + b2 - 1 = 0



So, the integers are ,
a = 0 , b = - 1  and c = 1

a = 0 , b = 1 and c = - 1

a = 1 , b = - 1 and  c = 0

a = 1 , b = 0 and c = - 1

a = - 1 , b = 0 and c = 1

a = - 1 , b = 1 and c = 0

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...