Question 33266
Let the two positive integers be x and y
given:
x+y = 20  which implies y = 20 - x
x*y = 91
x(20-x)=91
20x - {{{x^2}}}= 91
{{{x^2}}}-20x +91 = 0
{{{x^2}}} - 13x - 7x +91 = 0
x(x-3)-7(x-13) = 0
(x-7)(x-13)=0
(x-7) = 0 or (x-13) = 0
x = 7 or x = 13
y = 13 or y = 7

the smaller numbe is 7