Question

the difference between two positive integers is 4. if the smaller is added to the square of the larger, the sum is 52.

step 1 of 2: set up an equation to solve the given word problem.

Explanation:

Define variables for the integers

Using the Translating Word Problems to Quadratic Equations knowledge point
Let \(x\) be the smaller positive integer.
Since the difference between the two positive integers is \(4\), the larger positive integer is \(x + 4\).

Translate the relationship into an equation

Using the Translating Word Problems to Quadratic Equations knowledge point
The problem states: "If the smaller is added to the square of the larger, the sum is 52."
Smaller integer: \(x\)
Square of the larger integer: \((x + 4)^2\)
Equation:

$$x + (x + 4)^2 = 52$$

Answer:

The difference between two positive integers is 4. If the smaller is added to the square of the larger, the sum is 52.
Step 1 of 2 : Set up an equation to solve the given word problem.
<blank>\(x + (x + 4)^2 = 52\)</blank>