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