The sum of the squares of three consecutive natural numbers is 149. Find the numbers.

Let the three consecutive natural numbers be ‘a’, ‘a + 1’ and ‘a + 2’


a2 + (a + 1)2 + (a + 2)2 = 149


a2 + a2 + 2a + 1 + a2 + 4a + 4 = 149


a2 + 2a – 48 = 0


a2 + 8a – 6a – 48 = 0


a(a + 8) -6(a + 8) = 0


(a – 6)(a + 8) = 0


a = 6


Numbers are 6, 7, 8


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