Question

The sum of the two numbers is 22 and the sum of their squares is 221. find the numbers

Answer 1

Let x and x+1 be the consecutive integers.

Let x and x+1 be the consecutive integers. The sum of squares is:

Let x and x+1 be the consecutive integers. The sum of squares is: (x)² + (x+1)² = 221

Expand second term:

Expand second term: x² + x² + 2x + 1 = 221

Combine like terms:

Combine like terms: 2x² + 2x + 1 = 221

Subtract 221 from both sides to make quadratic form:

Subtract 221 from both sides to make quadratic form: 2x² + 2x - 220 = 0

Divide both sides by 2:

Divide both sides by 2: x² + x - 110 = 0

Factor:

Factor: (x + 11)(x - 10) = 0

Factor: (x + 11)(x - 10) = 0 x = -11 or x = 10

Factor: (x + 11)(x - 10) = 0 x = -11 or x = 10 Answers: 10 and 11 or -10 and -11