Problem
ALG-B1-M03-P003 Sum and Product
#3
★☆☆☆☆ Level 1 of 5
Find all pairs \(x,y\) such that \(x+y=8\), \(xy=15\).
Treat \(x,y\) as roots of a quadratic equation.
The numbers \(x,y\) are roots of \(t^2-8t+15=0\).
Thus \((t-3)(t-5)=0\). Therefore \((x,y)=(3,5)\) or \((5,3)\).
The key is to see the pair through Vieta's formulas.