Question

Two consecutive positive even numbers the sum of whose square is 340

Answer 1

Hi !!

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:

Step-by-step explanation:

Solution :-

Let the two consecutive even numbers be x and x + 2.

According to the Question,

⇒ (x)² + (x + 2)² = 340

⇒ x² + ² + 4 + 4x = 340

⇒ 2x² + 4x - 336 = 0

⇒ x² + 2x - 168 = 0

⇒ x² + 14x - 12x - 168 = 0

⇒ x(x + 14) - 12(x + 14) =0

⇒ (x - 12) (x + 14) = 0

⇒ x =  12, - 14 (As x can't be negative)

⇒ x = 12

1st number = x = 12

2nd number = x + 2 = 12 + 2 = 14

Hence, the numbers are 12 and 14.