For which of the following n is the number 2^74+2^2058+2^2n a perfect square?

• (2^37)2+2(2^37)(2^n)+(2^n)2= 2^74+2^2058+2^2n
  2^(38+n)=2^2058
  38+n=2058
  n=2058-38
  n=2020
  ANS:2020
  
• 12 years agoHelpfull: Yes(31) No(7)
• as (a+b)^2 is perfect square,
  apply (a+b)^2=a^2+b^2+2ab formula,
  compare given equation with the above formula,
  2^74 can be written as, (2^37)2
  2^2n can be written as, (2^n)2
  so,a=2^37,b=2^n
  2^2058=2ab=>2*(2^37)*(2^n)
  now,compare powers on both sides, then u'll get 2058=1+37+n
  so,n=2020
  2058=
  
  
• 12 years agoHelpfull: Yes(10) No(0)
• niki
  if 2020 is not in answer
  leave the ques this is a dummy question
• 12 years agoHelpfull: Yes(2) No(3)
• (2^37)^2+2*(2^37)*(2^n)+((2^n)^2)....a square+2*a*b+b square form
  so ...... 37+1+n=2058
  ans is 2020
• 12 years agoHelpfull: Yes(1) No(0)
• if 2020 is not the answer thn how v'll solve..? pls reply..
• 12 years agoHelpfull: Yes(0) No(0)
• not getting........pls explain well
• 12 years agoHelpfull: Yes(0) No(0)
• @ trishna
  not getting your solution.
  
• 12 years agoHelpfull: Yes(0) No(0)
• its a dummy ques.
  
• 12 years agoHelpfull: Yes(0) No(1)
• plz expln it clearly plzzzzz plzzzzz
• 12 years agoHelpfull: Yes(0) No(0)