If the product of two consecutive integers is 72, which of the following pairs c

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Question: If the product of two consecutive integers is 72, which of the following pairs could represent these integers?

Options:

Correct Answer: 6 and 7

Solution:

6 and 7 are consecutive integers whose product is 42, not 72.

If the product of two consecutive integers is 72, which of the following pairs could represent these integers?

If the product of two consecutive integers is 72, which of the following pairs could represent these integers?

Step 1: Understand what consecutive integers are. Consecutive integers are numbers that follow one after the other, like 1 and 2, or 6 and 7.
Step 2: Set up the problem. We need to find two consecutive integers whose product (when multiplied together) equals 72.
Step 3: Let the first integer be 'n'. Then the next consecutive integer will be 'n + 1'.
Step 4: Write the equation for their product: n * (n + 1) = 72.
Step 5: Expand the equation: n^2 + n = 72.
Step 6: Rearrange the equation to set it to zero: n^2 + n - 72 = 0.
Step 7: Factor the quadratic equation. We need two numbers that multiply to -72 and add to 1. These numbers are 9 and -8.
Step 8: Write the factored form: (n + 9)(n - 8) = 0.
Step 9: Solve for n: n + 9 = 0 gives n = -9, and n - 8 = 0 gives n = 8.
Step 10: Find the pairs of consecutive integers: If n = 8, then the integers are 8 and 9. If n = -9, then the integers are -9 and -8.
Step 11: Check the products: 8 * 9 = 72 and -9 * -8 = 72. Both pairs work.

Consecutive Integers – Consecutive integers are numbers that follow each other in order, such as n and n+1.
Product of Integers – The product of two integers is the result of multiplying them together.
Quadratic Equations – The problem can be framed as a quadratic equation where n(n+1) = 72.