The sum of the squares of two consective positive integers is 61. Find these two numbers.

**x = first consecutive positive integer**

x + 1 = second consecutive positive integer

x + 1 = second consecutive positive integer

x² + (x + 1)² = 61 {sum of squares of two consecutive positive integers is 61}

x² + (x + 1)(x + 1) = 61 {when squaring a binomial, multiply it by itself}

x² + x² + 2x + 1 = 61 {used the foil method}

2x² + 2x + 1 = 61 {combined like terms}

2x² + 2x - 60 = 0 {subtracted 61 from each side}

2(x² + x - 30) = 0 {factored a 2 out}

x² + x - 30 = 0 {set each factor equal to 0, 2 cannot be equal to 0}

(x + 6)(x - 5) = 0 {factored into two binomials}

x + 6 = 0 or x - 5 = 0 {set each factor equal to 0}

x = -6 or x = 5 {solved each equation for x}

x + 1 = -5 or x + 1 = 6 {substituted -6 and 5, in for x, into x + 1}

**5 and 6**

**are the two consecutive positive integers**

*- Algebra House*