Question 3 of 18, step 1 of 1
2/19
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the difference between two positive integers is 2. if the smaller is added to the square of the larger, the sum is 88. find the integers.
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smaller integer = 7

The larger integer = 9

Step-by-step 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

b

step-by-step explanation:

7,24

step-by-step explanation: