Question

One positive integer is 2 less than twice another. The sum of their squares is 628. Find the integers.

Answer 1

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let one of the integers be x,

other one = 2x - 2

now, according to question :

• 
  `{x}^(2) + (2x - 2) {}^(2) = 628`

• 
  `{x}^(2) + 4 {x}^(2) + 4 - 8 x = 628`

• 
  `5 {x}^(2) - 8x = 628 - 4`

• 
  `5 {x}^(2) - 8x = 624`

• 
  `5 {x}^(2) - 8x - 624 = 0`

• 
  `5 {x}^(2) - 60 x+ 52 x- 624 = 0`

• 
  `5x(x - 12) + 52(x - 12) = 0`

• 
  `(5x + 52)(x - 12) = 0`

now, since the Integers are positive so the value obtained from (5x + 52) = 0 can't hold true.

so, x - 12 = 0

• 
  `x = 12`

the first number is :

• 
  `x = 12`

second number is :

• 
  `2x - 2`

• 
  `(2 * 12) - 2`

• 
  `24 - 2`

• 
  `22`