Math and Arithmetic

# What is the product of 96 with their difference is 10?

###### Wiki User

###### May 27, 2009 9:08AM

6 and 16

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###### Asked in Math and Arithmetic

### What two numbers have the product of 96 and a difference of 10 when you show how to solve?

You can set this up as follows...
Let the two numbers be defined as x and y. Then,
x * y = 96
x - y = 10
x = 96/y and substitute
96/y - y = 10
rearranging yields a quadratic equation
96 - y^2 = 10y or
y^2 + 10y - 96 = 0
The solution(s) to the quadratic equation are given by:
y = (-b +/- sqrt(b^2-4ac)) / 2a
y = (-10 +/- sqrt(100 - 4(-96))) / 2
y = (-10 + 22 ) / 2 = 6
y = (-10 - 22 ) / 2 = -16
So, y can be 6 or -16
making x = 16 or -6
So you have two answers, (x,y) = (16,6) or (x,y) = (-6,-16)