Question

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

Answer 1

Answer:

The two consecutive even numbers are 12 and 14.

Step-by-step explanation:

Set up the equation, which turns out to be a quadratic, solve for n:

$(2n)^2+(2(n+1))^2=340\\4n^2+4n^2+8n+4=340\\8n^2+8n-336=0\\n^2+n-42=0\\\implies (n_1=-7),\,\,\,n_2=6$

We are looking for positive even numbers, so the solution -7 is not valid. The solution for n is 6, and the two consecutive even numbers are:

2*6=12

2*7=14

Test: 12*12 + 14*14 = 340