Two consecutive positive numbers are such that the sum of their squares is 113. find the two numbers

Answer: 7 and 8

Step-by-step explanation:

Let x represent the first number, then x + 1 is the other number.

(x) ² + (x + 1) ² = 113

x² + x² + 2x + 1 = 113 expanded (x + 1) ²

2x² + 2x + 1 = 113 added like terms

2x² + 2x - 112 = 0 subtracted 113 from both sides

x² + x - 56 = 0 divided both sides by 2

(x + 8) (x - 7) = 0 factored polynomial

x + 8 = 0 x - 7 = 0 applied zero product property

x = - 8 x = 7 solved for x

↓

not valid since the restriction is that x > 0 (a positive number)

So, x = 7 and x + 1 = (7) + 1 = 8