Question 255742
Let X = even integer and x+2 is the next even integer.
(i) {{{x^2 + (x+2)^2 = 100}}}
step 1 - expand (i) to get
(ii) {{{x^2 + x^2 + 4x + 4 = 100}}}
step 2 - combine like terms to get
(iii) {{{2x^2 + 4x + 4 = 100}}}
step 3 set = 0 and solve by factoring to get
(iv) {{{2x^2 + 4x - 96 = 0}}}
{{{(2x+16)(x-6)=0}}}
(2x+16) = 0 - - > x = -8
(x-6) = 0 - - - -> x = 6
since they are positive, we get x = 6 and x+2 = 8.