**Problem Statement:**The difference between the squares of two consecutive positive integers is **17**. Find the integers. *(Hint: Let x and x + 1 represent the consecutive integers.)***Solution Steps:**1. **Let the integers be x and x + 1:** - We are given two consecutive integers. Let's denote the smaller integer by \( x \) and the larger integer by \( x + 1 \).2. **Expression for squares:** - The square of the smaller integer is \( x^2 \). - The square of the larger integer is \( (x + 1)^2 \).3. **Difference between squares:** - According to the problem, the difference between their squares is 17. Therefore, we can set up the equation: \[ (x + 1)^2 - x^2 = 17 \]4. **Expand and simplify the equation:** - Expanding the left-hand side, we get: \[ (x^2 + 2x + 1) - x^2 = 17 \] - Simplify to: \[ 2x + 1 = 17 \]5. **Solve for x:** - Isolate \( x \) by subtracting 1 from both sides: \[ 2x = 16 \] - Divide both sides by 2: \[ x = 8 \]6. **Find the consecutive integers:** - The smaller value is \( x = 8 \). - The larger value is: \[ x + 1 = 9 \]**Answer Boxes:**- **Smaller value:** [ 8 ]- **Larger value:** [ 9 ]By plugging these values into the given relationship, we can verify that the difference between their squares is indeed 17:\[(9)^2 - (8)^2 = 81 - 64 = 17\]Thus, the consecutive positive integers are 8 and 9.

Name: **Problem Statement:**The difference between the squares of two conse
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Problem Statement:**The difference between the squares of two consecutive positive integers is **17**. Find the integers. *(Hint: Let x and x + 1 represent the consecutive integers.)***Solution Steps:**1. **Let the integers be x and x + 1:** - W