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

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

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

Steps: 11

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.