Question 206937
Let the two numbers be x and y, then...
1) {{{x+y = 23}}} "the sum of two numbers is 23.."
2) {{{x*y = 132}}} "...their product is 132."
Rewrite equation 1) as: {{{x = 23-y}}} and substitute this for x into equation 2).
2a) {{{(23-y)*Y = 132}}} Solve for y.
2a) {{{23y-y^2 = 132}}} Rearrange into standard quadratic form.
2a) {{{y^2-23y+132 = 0}}} Factor.
2a) {{{(y-12)(y-11) = 0}}} Apply the zero product rule.
{{{y-12 = 0}}} or {{{y-11 = 0}}} which means that:
{{{y = 12}}} or {{{y = 11}}}
The two numbers are 11 and 12.