The sum of two numbers is 19, and their product is 78. What is the smaller number?
1 Answer
Explanation:
Let the numbers be
Given:
#x + y = 19 -># Equation 1
#x*y = 78 -># Equation 2
#y = 78/x -># from equation 2
Substituting
#x + 78/x = 19#
#x^2 + 78 = 19x#
#x^2 - 19x + 78 = 0#
#x^2 - 6x - 13x + 78 = 0#
#x(x-6) -13(x-6) = 0#
#(x-6)(x-13)=0#
#x= 13# or#x=6#
The smallest no is