Question 432719
Let the two numbers be m and n.
1) {{{m^2+n^2 = 100}}} "The sum of the squares of two numbers is 100."
2) {{{m + n = 2}}} "The sum of the numbers is 2." Rewrite this as {{{m = 2-n}}} and substitute for m in equation 1).
1a) {{{(2-n)^2+n^2 = 100}}} Simplify.
2b) {{{4-4n+n^2+n^2 = 100}}}
2c) {{{2n^2-4n+4 = 100}}} Subtract 100 from both sides.
2d) {{{2n^2-4n-96 = 0}}} Solve by factoring.
2e) {{{2(n^2-2n-48) = 0}}}
2f) {{{2(n+6)(n-8) = 0}}}
2g) {{{n+6 = 0}}} or {{{n-8 = 0}}}
So, {{{n = -6}}} or {{{n = 8}}}
The two numbers are -6 and 8.