Answer:
4, 5, and 6
Step-by-step explanation:
- let x, (x+1), and (x+2) be the consecutive integers.
- It says that the product of the first two [x and (x+1)] is 10 less than the product of the last two [(x+1) and (x+2)]
- Translate to Mathematical statement.
x (x + 1) = (x + 1)(x + 2) - 10
x² + x = x² + 3x + 2 - 10
x² + x = x² + 3x - 8
x² - x² + x = x² - x² + 3x - 8 (SPE)
x = 3x - 8
x - 3x = 3x - 3x - 8 (SPE)
-2x = -8
-2x/-2 = -8/-2 (DPE)
x = 4
- Use the value of x to get the other two integers.
x = (4) = 4
(x + 1) = (4 + 1) = 5
(x + 2) = (4 + 2) = 6
x (x + 1) = (x + 1)(x + 2) - 10
4 (4 + 1) = (4 + 1)(4 + 2) - 10
4 (5) = (5)(6) - 10
20 = 30 - 10
20 = 20 ✓
Therefore, the three consecutive integers are:
4, 5, and 6
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