Find two consecutive positive integers such that the sum of their squares is 145.

Question

Solve the word problem.

Answer 1

"two consecutive positive integers"  means  we can represent them as   (x)  and  (x+1).

 

"sum of their squares is 145"   means

      (x)² + (x+1)²      = 145

 

     x²   +    x² + 2x + 1 = 145    [use F-O-I-L]

    2x² + 2x - 144 = 0                [collect terms; subtract 145 from both sides]

    x² + x - 72 = 0                 [divide by 2 to simplify]

   (x+9)(x-8) = 0                [either factor or use quadratic formula]

  Either x=-9 or x=8 or both      [multiplicative property of zero]

     Ignore x=-9                      ["positive integers"]

    x = 8

  x+1 = 9

 

The consecutive positive integers are 8 and 9.

 

Check:

   Is 8² + 9² = 145   ?

       64 + 81 = 145   ?

          145 = 145   ?yes