SOLUTION: The square of one number is 23 less than the square of a second number. If the second number is 1 more than the first, what are the two numbers? If x represents the smaller numb

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Question 975672: The square of one number is 23 less than the square of a second number. If the second number is 1 more than the first, what are the two numbers?
If x represents the smaller number, then which of the following quadratic equations represents the word problem?
Answer by algebrahouse.com(1659)   (Show Source): You can put this solution on YOUR website!
x = one number
x + 1 = second number {second number is 1 more than the first}

x² = (x + 1)² - 23 {square of one number is 23 less than square of second}
x² = x² + 2x + 1 - 23 {squared the binomial with the foil method}
0 = 2x - 22 {subtracted x² from each side and combined like terms}
2x = 22 {added 22 to each side}
x = 11 {divided each side by 2}
x + 1 = 12 {substituted 11, in for x, into x + 1}

11 is the first number
12 is the second number

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