Question

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 1

If we're using x to describe this word problem, then what we can first say is that the larger number is x + 1 as it is 1 more than the first number. We also know that x^2 = (x + 1)^2 + 23, which is hopefully one of your options for the second part of the question. To find the two numbers, we just need to solve for x

x^2 = x^2 + 2x + 24
- x^2
0 = 2x + 24
- 24
-24 = 2x
÷ 2
-12 = x

So now we know that the first number is -12, and the second number is one more than that, which is -11. I hope this helps!