Find two consecutive even integers sum of whose squares is 340

(12) ² + (14) ² = 144 + 196 = 340

Let two consecutive integers be 2x and 2x + 2

Acc. to question

(2x) ^2 + (2x+2) ^2 = 340

4 (x^2 + 1 + 8x) = 340

x^2 + 8x - 84 = 0

x^2 + 14x - 6x - 84 = 0

x (x + 14) - 6 (x + 14) = 0

(x+14) (x - 6) = 0

if (x+14) = 0

x=-14 (not possible)

take x-6=0

x = 6

therefore two consecutive even number are 12, 14