Question

one number is 2 more than another. the difference between their squares is 52. what are the numbers?

smaller number =
larger number =

Explanation:

Define variables and set up equations

Using the Difference of Squares Word Problems knowledge point
Let \(x\) be the smaller number.
The larger number is \(x + 2\).
The difference between their squares is 52:

$$(x + 2)^2 - x^2 = 52$$

Expand the squared binomial

Using the Square of a Binomial Sum knowledge point

$$(x + 2)^2 = x^2 + 4x + 4$$

Substitute this back into the equation:

$$x^2 + 4x + 4 - x^2 = 52$$

Solve for the smaller number

Using the Difference of Squares Word Problems knowledge point

$$
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$$

Find the larger number

Using the Difference of Squares Word Problems knowledge point

$$x + 2 = 12 + 2 = 14$$

Answer:

One number is 2 more than another. The difference between their squares is 52. What are the numbers?

smaller number = <blank>12</blank>

larger number = <blank>14</blank>