Given:
x + (15 - x) = 15
x^2 + (15 - x)^2 = 113
Find:
x and (15 - x)
Substitute the first equation into the expression for (15 - x) to get:
x^2 + (15 - x)^2 = 113
x^2 + 225 + x^2 - 30x + x^2 = 113
3x^2 - 30x + 112 = 0
Factor the quadratic equation:
(x - 7)(x - 8) = 0
Solve for x:
x = 7 or x = 8
Therefore, the two numbers are x = 7 and (15 - x) = 8.