Question

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

Answer 1

Let one of the number be x then the other number be x + 2.

Then according to question,

\[x^2 + \left( x + 2 \right)^2 = 340\]

\[ \Rightarrow x^2 + x^2 + 4x + 4 = 340\]

\[ \Rightarrow 2 x^2 + 4x - 336 = 0\]

\[ \Rightarrow x^2 + 2x - 168 = 0\]

\[ \Rightarrow x^2 + 14x - 12x - 168 = 0\]

\[ \Rightarrow x(x + 14) - 12(x + 14) = 0\]

\[ \Rightarrow (x - 12)(x + 14) = 0\]

\[ \Rightarrow x - 12 = 0 \text { or } x + 14 = 0\]

\[ \Rightarrow x = 12 \text { or } x = - 14\]

Since, x being an even number,

Therefore, x = 12.

Then another number will be \[x + 2 = 12 + 2 = 14\]

Thus, the two consecutive even numbers are 12 and 14.