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