Question

The sum of squares of 2consecutive even numbers is 340 . what are the numbers​

Answer 1

Let the two consecutive positive even integers be x and  x+2

given ,

x² + (x+2)² = 340

x² + x² + 4x + 4 = 340

2x² + 4x + 4 - 340 = 0

2x² + 4x - 336 = 0               ----> dividing by 2

x² + 2x - 168 = 0

splitting the middle term,

x² +14x - 12x - 168

x(x + 14)  - 12(x + 14)

(x+14) (x - 12)

x = 12 

hence , 

the numbers are ,

x = 12

x + 2 = 12 + 2 = 14

12 and 14

Answer 2

Answer:

two consecutive even number is 12 , 14

Step-by-step explanation:

let two even consecutive number = x , x+2

x² + (x + 2)² = 340

x² + x² + 4 + 4x = 340

2x² + 4x + 4 - 340 = 0

2x² + 4x - 336 = 0

divide by 2

x² + 2x - 168 = 0

x² + (14 - 12)x - 168 = 0

x² + 14x - 12x - 168 = 0

x(x + 14).-12(x + 14) = 0

(x - 12)(x + 14) = 0

x - 12 = 0 , x + 14 = 0

x = 12 , x = -14

x = -14 is not satisfied number

so, two consecutive number is

x = 12

x + 2 = 12 + 2 = 14