The sum of the squares of two consecutive even numbers is 340. Find th

1.	The sum of the squares of two consecutive even numbers is 340. Find the numbers.
Answer» Let the consecutive even integers be ‘a’ and a + 2 ⇒ a² + (a + 2)²= 340 ⇒ 2a² + 4a – 336 = 0 ⇒ a² + 2a – 168 = 0 ⇒ a² + 14a – 12a – 168 = 0 ⇒ a(a + 14) – 12(a + 14) = 0 ⇒ (a – 12)(a + 14) = 0 Thus, a = 12 or – 14 Consecutive even integers are 12, 14 or -14, - 12

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

Answer»

Let the consecutive even integers be ‘a’ and a + 2

⇒ a² + (a + 2)²= 340

⇒ 2a² + 4a – 336 = 0

⇒ a² + 2a – 168 = 0

⇒ a² + 14a – 12a – 168 = 0

⇒ a(a + 14) – 12(a + 14) = 0

⇒ (a – 12)(a + 14) = 0

Thus, a = 12 or – 14

Consecutive even integers are 12, 14 or -14, - 12