Problem
NT-B1-M11-P008 Product After Adding
#8
★★☆☆☆ Level 2 of 5
Solve \(xy+x+y=23\) in positive integers.
Add \(1\) to both sides.
We get \((x+1)(y+1)=24\). Factor pairs of \(24\) greater than \(1\) are \((2,12),(3,8),(4,6),(6,4),(8,3),(12,2)\). Hence \((x,y)=(1,11),(2,7),(3,5),(5,3),(7,2),(11,1)\).
Builds the habit of completing to a product.