SOLUTION: The difference between two numbers is 9 and the product of the numbers is 162. Find the two numbers.

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Question 918203: The difference between two numbers is 9 and the product of the numbers is 162. Find the two numbers.
Answer by srinivas.g(540)   (Show Source): You can put this solution on YOUR website!
let x , y be the 2 numbers
as per the data x-y =9
and x*y = 162
but x-y =9
x = 9+y
put x= 9+y in x*y = 162
(9+y) *y =162
9*y+y*y= 162
9y+y^2 =162
y^2+9y =162
subtract 162 on both sides
y^2 +9y -162 =162-162
y^2+9y-162 =0
solve the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=729 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 9, -18. Here's your graph:


so y is either 9 or -18
if y =9 then x = 9+y=9+9=18
so numbers x =18 & y =9
if y =-18 then x= 9+y=9-18 =-9
so numbers x =-9 & y=-18
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