Hello,
Let's f the age of the father
a the age of the oldest son
y the age of the youngest son
f=a+20
a=y+2 ==>f=y+22
In 3 years: father->f+3=y=25
oldset son ->a+3=y+5
youngest son->y+3
Product of the ages of the sons in 3 years: (y+5)(y+3)=y²+8y+15
so y²+8y+15=11(y+25)+10
==>y²+8y+15=11y+275+10
==>y²-3y-270=0
Δ=9+4*270=1089=33²
y=(3+33)/2=18 or (y=(3-33)/2 <0 to exclude)
The youngest son is 18 years's old
