Problem
ALG-B1-M03-P006 A Pair from Sum of Squares
#6
★★☆☆☆ Level 2 of 5
Find \(x,y\) if \(x+y=7\), \(x^2+y^2=25\).
First find \(xy\).
From \(x^2+y^2=(x+y)^2-2xy\), we get \(25=49-2xy\), hence \(xy=12\).
Then \(x,y\) are roots of \(t^2-7t+12=0\), so \(t=3\) or \(t=4\). Answer: \((3,4)\), \((4,3)\).
The system is solved without guessing.