Question 122744
Try this:
Let x = the first even number, the x+2 = the next consecutive even number.
From the problem description, you can write:
{{{x^2+(x+2)^2 = 452}}} Simplify this.
{{{x^2+x^2+4x+4 = 452}}}
{{{2x^2+4x+4 = 452}}} Subtract 452 from both sides.
{{{2x^2+4x-448 = 0}}} Factor out a 2 to ease the calculations a bit.
{{{2(x^2+2x+224) = 0}}} so that:
{{{x^2+2x+224 = 0}}} Solve this quadratic by factoring:
{{{(x-16)(x+14) = 0}}} so then...
{{{x = 16}}} or {{{x = -14}}}
Now since the problem did not restrict the answers to positive integers, there are two solutions:
1) {{{x = 14}}} and {{{x = 16}}}
2) {{{x = -16}}} and {{{x = -14}}}