Question 521728
Let the two numbers be A and B. Then...
{{{A+B = 9}}} and...
{{{A*B = 20}}}
Rewrite the first equation as:
{{{A = 9-B}}} and substitute for a in the second equation.
{{{(9-B)*B = 20}}} Simplify.
{{{9B-B^2 = 20}}} Rewrite as a quadratic equation in standard form.
{{{-B^2+9B-20 = 0}}} Apply the quadratic formula: {{{x = (-b+-sqrt(b^2-4ac))/2a}}} (x is really B, one of the two numbers). In this problem, from the quadratic equation, a = -1, b = 9, and c = -20.
{{{B = (-9+-sqrt(9^2-4(-1)(-20)))/2(-1)}}}
{{{B = 4.5+(-0.5)}}} or {{{B = 4.5-(-0.5)}}}
{{{B = 4}}} or {{{B = 5}}}
The two numbers are 4 and 5.