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Home / Doubts and Solutions/JEE/Mathematics

Ques 13

Asked by rbhatt16 20th October 2017, 12:27 PM
Answered by Expert
Answer:
a = (6)n  ,  b = (8)n and c = (4)2n   where (r)n =rrrr...(n digit number)
 
By Intution a2 + b + c  is not equal to zero, since sum of positive integers will not be zero
 
Hence ' a2  + b + c = 0 '  can be excluded.
 
let us consider n = 1 and find the relation of a2  + b - c
 
begin mathsize 12px style a squared plus b minus c space equals space open square brackets open parentheses 6 close parentheses subscript n close square brackets squared plus open square brackets open parentheses 8 close parentheses subscript n close square brackets minus open square brackets open parentheses 4 close parentheses subscript 2 n end subscript close square brackets space equals space 6 squared open square brackets open parentheses 1 close parentheses subscript n close square brackets squared plus 8 open square brackets open parentheses 1 close parentheses subscript n close square brackets minus 4 open square brackets open parentheses 1 close parentheses subscript 2 n end subscript close square brackets space space space equals space space 36 open square brackets open parentheses 1 close parentheses subscript n close square brackets squared plus 8 open square brackets open parentheses 1 close parentheses subscript n close square brackets minus 4 open square brackets open parentheses 1 close parentheses subscript 2 n end subscript close square brackets l e t space u s space h a v e space n space equals space 1 semicolon space t h e n space 36 open square brackets open parentheses 1 close parentheses close square brackets squared plus 8 open square brackets open parentheses 1 close parentheses close square brackets minus 4 open square brackets open parentheses 11 close parentheses close square brackets space equals space 36 plus 8 minus 44 space equals space 0 semicolon H e n c e space a squared plus b minus c space equals space 0 space s a t i s f i e d l e t space u s space c h e c k space t h i s space c o n d i t i o n space a g a i n space w i t h space n space equals space 2 semicolon 36 open square brackets open parentheses 11 close parentheses close square brackets squared plus 8 open square brackets open parentheses 11 close parentheses close square brackets minus 4 open square brackets open parentheses 1111 close parentheses close square brackets equals space left parenthesis 36 cross times 121 right parenthesis plus left parenthesis 8 cross times 11 right parenthesis minus 4 x 1111 space equals space 4356 plus 88 minus 4444 space equals space 0 end style
 
Hence the answer (b) a2  + b - c is the correct answer
Answered by Expert 14th December 2017, 5:08 PM
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