Mishita Dharia - Quadratics

The squares of two consecutive integers are added. The sum of their squares is 164. What are the integers?

 

Let ‘x’ represent the first integer.

Let ‘x+1’ represent the second integer.

 

x^2 + (x+1)^2 = 61

x^2 + (x+1)(x+1) = 61

x^2 + x^2 + 2x + 1 = 61

2x^2 + 2x + 1 – 61 = 0

2x^2 + 2x– 60 = 0

 

[Find the zeros/x-ints by either factoring or using the quadratic formula]

 

2x^2 + 2x – 60 = 0

2(x^2 + 1x – 30) = 0

 

(-5) x 6 = 30

(-5) + 6 = 1

 

2(x – 5)(x + 6)

 

x – 5 = 0

x = 5

 

If x = 5 then x + 1 = 5 + 1 = 6

 

x+6 = 0

x = -6

If x = -6 then x + 1 = (-6) + 1 = -5

 

Therefore the integers can be 5 & 6 or -6 & -5.