write an equation representing the fact that the sum of the squares of two consecutive integers is 313

Question

use X to represent the smaller integer 

Answer 1

The two integers are x and x + 1.

 

x² + (x + 1)² = 313

 

You can solve for x.

 

x² + (x² + 2x + 1) = 313

 

2x² + 2x - 312 = 0

 

Divide by 2 to simplify a little:

 

x² + x - 156 = 0

 

Factor the equation above and get

 

(x - 12)(x + 13) = 0

 

This gives two solutions:  x = 12 or x = -13

 

Then x + 1 = 13 or -12

 

You have two pairs of consecutive integers that satisfy the conditions:  12 and 13; or -13 and -12

 

You can test to verify that both pairs satisfy the conditions.

Answer 2

X² + (X+1)² = 313