Question : The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is:
Option 1: 30
Option 2: 33
Option 3: 36
Option 4: 45
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Correct Answer: 33
Solution : Let the consecutive numbers be (x – 1), x and (x + 1). According to the question, (x–1) 2 + x 2 + (x+1) 2 = 365 ⇒ (x 2 – 2x + 1) + x 2 + (x 2 + 2x + 1) = 365 ⇒ 3x 2 = 365 – 2 ⇒ 3x 2 = 363 ⇒ x 2 = 121 ⇒ x = 11 So, the numbers are 10, 11 and 12. The sum of the numbers = 10 + 11 + 12 = 33 Hence, the correct answer is 33.
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