consecutive numbers

Question

Find three consecutive even numbers if it is known that the sum of the squares of the first 2 is equal to the square of the third number.

Find three consecutive even numbers if it is known that the sum of the squares of the first 2 is equal to the square of the third number.

Answer 1

Please stop posting the question twice. Thank you.

 

Three consecutive even integers X, X+2, X+4

 

X^2 + (x+2)^2 = (x+4)^2

 

x^2 + (x^2 + 4x + 4) = x^2 + 8x + 16

 

2x^2 + 4x + 4 = x^2 + 8x + 16

 

x^2 - 4x - 12 = 0  <-- everything to the left side

 

(x - 6)(x+2) = 0

 

x=6 or x = -2

 

First case:  6,8, and 10

 

    36 + 64 = 100 = 10^2

 

Second case:

 

 -2, 0 , and 2

 

(-2)^2 + 0^2 = 4 + 0 = 4 = 2^2

 

 

So there are 2 sets of 3 consecutive integers that meet this condition:

  6,8, and 10    and -2,0, and 2