Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number.

• this is a property for number any three consecutive whole numbers ............
  
  so , any three consecutive whole numbers can be the answer
  
• 13 years agoHelpfull: Yes(42) No(10)
• It can be any set of three consecutive numbers.
  If numbers are (x-1),x , (x+1)
  then (x+1)*(x-1) = x^2-1 which is less than square of middle number by 1.
• 13 years agoHelpfull: Yes(15) No(5)
• ans : 2n,2n+1,2n+2 where n = 1,2,3...
• 13 years agoHelpfull: Yes(8) No(5)
• numbers are 2,3,4
  3*3=4*2+1
  middle number is 3
• 13 years agoHelpfull: Yes(7) No(13)
• There is no unique solution
  :
  let x = the middle number
  then
  (x-1) = the 1st number
  and
  
  (x+1) = the 3rd number
  :
  x^2 = ((x-1)*(x+1)) + 1
  
  x^2 = x^2 - 1 + 1
  :
  x^2 = x^2
  Which means this is true for any 3 consecutive numbers even, -1, 0 +1
  :
  Try a few like; 142, 143, 144: 143^2 = 20449, 142*144 = 20448
• 11 years agoHelpfull: Yes(5) No(4)
• 2 or 3 (eg.123 or 234)
• 9 years agoHelpfull: Yes(1) No(0)
• 7 8 9 7*9=63 8*8=64
  
• 8 years agoHelpfull: Yes(1) No(0)
• i think middle number is 1.
  
• 9 years agoHelpfull: Yes(0) No(0)
• its says ..which number satisfy the following equation
  (x^2) - 1 = (x -1)(x+1)
  but this is a universal formulae... so answer can be any.
  
  36-1 = 7*5
  18^2 - 1 = 17*19
  ... so on
• 8 years agoHelpfull: Yes(0) No(0)
• any three consecutive numbers
• 8 years agoHelpfull: Yes(0) No(0)
• three consecutive numbers be 765
  product = 7*5=35;
  square= 6*6 = 36
  therefore 36-35 =1.
• 7 years agoHelpfull: Yes(0) No(0)
• It can be any set of three consecutive numbers.
  If numbers are (x-1),x , (x+1) ,he told that square of x is differ by 1 to the product of residue numbers
  then x^2=(x+1)(x-1)+1,so x can be any number
• 7 years agoHelpfull: Yes(0) No(0)