MATH SOLVE

3 months ago

Q:
# Question 3 of 18, Step 1 of 12/19CorrectThe 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.AnswerHow to enter your answerKeypadsmaller integer =larger integer =Submit Answer© 2019 Hawkes LearningNe

Accepted Solution

A:

Answer:smaller integer = 7The larger integer = 9Step-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