Find two consecutive positive integers,Sum of whose squares is 925

Question

Solve it with quadratic formula

Answer 1

Let the integers be x and (x + 1)

 

x² + (x + 1)² = 925

 

x² + x² + 2x + 1 = 925

 

2x² + 2x + 1 = 925

 

2x² + 2x - 924 = 0

 

x² + x - 462 = 0

 

This equation is in the form

 

Ax² + Bx + C = 0

 

a = 1, b = 1, c = -462

 

Now, plug these values into the Quadratic Formula

 

x = [-b ± sqrt (b² - 4ac)]/2a