The sum of two numbers is 19, and their product is 78. What is the smaller number?

1 Answer
jags · Stefan V.
Jun 26, 2016

#6#

Explanation:

Let the numbers be #x#, #y#.

Given:

#x + y = 19 -># Equation 1

#x*y = 78 -># Equation 2

#y = 78/x -># from equation 2

Substituting #y# in equation 1, we get

#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 #6#.

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