



 
Hi Marj, Suppose the two numbers are $x$ and $y.$ Their sum is 22 so \[x + y = 22.\] Their product is 125 and this gives you another equation. Solve the first equation for y, substitute into the second equation and simplify. Solve the resulting quadratic. If you have a hard time believing the result use some computer software or a graphing calculator to plot the quadratic. Penny
Eliminate one variable: $x+y = 22 \rightarrow y = 22x$ Plug in: $125 = x(22x);$ Tidy up: $x^2  22x + 125 = 0$ Now, the quadratic formula requires you to take the square root of $b^2  4ac$ where (here)$ a=1, b=22, c = 125$ Can you do this? (If not, there is no solution.) Good Hunting!
Let x an y be the two real numbers with the desired properties \[x = \frac{22 \pm \sqrt{484  500}}{2}\] Paul  


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