Answer:
smaller integer = 7
The larger integer = 9
Explanation:
* Lets explain how to solve the problem
- There are two integers
- Assume that the smaller is x and the larger is y
- The difference between them is 2
∵ The y is the larger and x is the smaller
∵ y - x = 2 ⇒ (1)
- If the smaller is added to the square of the larger, the sum is 88
∵ The square of the larger is y²
∴ x + y² = 88 ⇒ (2)
* Lets use the substitute method to solve the problem
- Use equation (1) to find x in terms of y
∵ y - x = 2 ⇒ add x to 2 sides and subtract 2 from both sides
∴ y - 2 = x ⇒ switch the two sides
∴ x = y - 2 ⇒ (3)
- Substitute x in equation (2) by equation (3)
∴ (y - 2) + y² = 88 ⇒ subtract 88 from both sides
∴ y - 2 + y² - 88 = 0 ⇒ add the like terms and arrange the terms
∴ y² + y - 90 = 0
* Lets factorize it
∵ y² = y × y
∵ 90 = 9 × 10
∵ y × 9 = 9y and y × 10 = 10y
∵ 10y - 9y = y
∴ y² + y - 90 = (y + 10)(y - 9)
∵ y² + y - 90 = 0
∴ (y + 10)(y - 9) = 0
- Equate each bracket by 0
∴ y + 10 = 0 and y - 9 = 0
∵ y + 10 = 0 ⇒ subtract 10 from both sides
∴ y = -10
∵ y - 9 = 0 ⇒ add 9 to both sides
∴ y = 9
∵ The numbers are positive we will rejected y = -10
∴ y = 9
- Substitute the values of y in equation (3) to find x
∵ x = y - 2
∴ x = 9 - 2 = 7
∴ x = 7
* The smaller integer = 7
* The larger integer = 9