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 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 Comments are closed.

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