The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.
Let the consecutive multiples of 7 be ‘a’ and a + 7
⇒ a2 + (a + 7)2 = 637
⇒ 2a2 + 14a – 588 = 0
⇒ 2a2 + 42a – 28a – 588 = 0
⇒ 2a(a + 21) – 28(a + 21) = 0
⇒ (2a – 28)(a + 21) = 0
Thus, a = 14
Consecutive multiples of 7 are 14, 21