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Find 3 consecutive even numbers where the product of the smaller two number is 52 less than the square of the largest number?
Updated: 9/17/2023
6, 8, 10.
102 is 100. Subtract 52 from that, and you get 48, which is 6.8
Method: call the smaller of the unknown even numbers n. Then, from the problem statement, n(n+2) + 52 = (n + 4)2. Multiplying out yields n2 + 2n + 52 = n2 + 8n + 16. Collecting like terms from both sides yields 6n = 36 or n = 6.
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