Find the two integers

Question

the sum of the squares of two consecutive odd integers is 74. Find the two integers 

Answer 1

Let X = first integer

X+2 = second integer

 

X² + (X+2)² = 74

 

X² + X² + 4X + 4 = 74

 

2X² + 4X = 70

 

2 (X² + 2X) = 70

 

X² + 2X = 35

 

X² + 2X - 35 = 0

 

(X - 5) (X + 7) = 0

 

X = 5 or -7

 

If X = 5, then X+2 = 7, check to see if their squares add to 74:

 

5² + 7² = 25 + 49 = 74

 

Thus 5 and 7 are consecutive odd integers whose squares add to 74.

 

ALSO, however:

 

(-7)² + (-5)² would also equal 74 and as you read the number line left to right, -7 and -5 are consecutive odd integers.