Question

Find the consecutive even integers whose squares have the sum 340.

Answer 1

Let the consecutive even integers be 2x and 2x + 2.

Then according to the given hypothesis,

(2𝑥)² + (2𝑥 + 2)² = 340

⇒ 8𝑥² + 8𝑥 - 336 = 0

⇒ 𝑥² + 𝑥 - 42 = 0

⇒ 𝑥² + 7𝑥 - 6𝑥 - 42 = 0

⇒ 𝑥(𝑥 + 7) - 6(𝑥 + 7) = 0

⇒ (𝑥 + 7)(𝑥 - 6) = 0

⇒ x = -7 or x = 6

Considering, the positive integers of x.

⇒ x = 6; 2x = 12 and 2x + 2 = 14.

∴ The two consecutive even integers are 12 and 14.