The smith have 2 children. the sum of their ages is 21, and the product of their ages is 110. how old are the children

X+y=21
xy=110

x+y=21
subtract x form both sides
y=21-x
subsitute
x(21-x)=110
21x-x^2=110
add x^2-21x to both sides
0=x^2-21x+110
use quaratic formula which is
(-b+/-√(b^2-4ac)/(2a)=x
when you have it in the format of ax^2+bx+c=0 so

a=1
b=-21
c=110

input
two equations
(-(-21)+√(-21^2-4 times 1 times 110))/(2) or (-(-21)+√(-21^2-4 times 1 times 110))/2

the answer is
10 or 11

that is the answer

the ages are 10 and 11