today star questions
1. 2^74+2^2048+2^2n is a perfect square what is
the largest possible number n..

• 2^74+2^2048+2^2n=a^2+2ab+b^2
  therefore,a=2^37,b=2^n nd 2ab=2^2048
  2^38*2^n=2^2048
  38+n=2048
  n=2010
• 11 years agoHelpfull: Yes(55) No(1)
• since, (a+b)^2=a^2+b^2+2ab
  2^74+2^2n+2^2048=(2^37)^2+(2^n)^2+2^2048
  2*(2^37)*(2^n)=2^2048
  2^(1+37+n)=2^2048
  since base are same ,equating powers,we get
  1+37+n=2048
  38+n=2048
  n=2010
• 11 years agoHelpfull: Yes(19) No(0)
• 2010 on solvg it is in the form f (a+b)^2
• 11 years agoHelpfull: Yes(1) No(0)
• n=2010
  as a^2+(2*a*b)+b^2
  so 2^37+2*2^37*2^n+2^n
  now 2048-(1+37)=2010
• 11 years agoHelpfull: Yes(0) No(0)
• (2^37)^2 + 2*2^37*2^n +(2^n)^2= a^2 +2ab +b^2
  2*2^37*2^n=2ab
  2^38+n=2^2048
  n=2010ans
  
• 11 years agoHelpfull: Yes(0) No(1)
• (2^37)^2 + (2^n)^2+ 2^2048
  let a= 2^37
  b= 2^n
  2ab= 2^2048
  2*2^37*2^n=2^2048
  2^(1+37+n)=2^2048
  38+n=2048
  n=2010
• 11 years agoHelpfull: Yes(0) No(0)