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

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The difference between two numbers is 9 and the product of the numbers is 162. Find the two numbers.       Log On


   

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) About Me  (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 ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B9y%2B-162+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%289%29%5E2-4%2A1%2A-162=729.

Discriminant d=729 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+729+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%289%29%2Bsqrt%28+729+%29%29%2F2%5C1+=+9
y%5B2%5D+=+%28-%289%29-sqrt%28+729+%29%29%2F2%5C1+=+-18

Quadratic expression 1y%5E2%2B9y%2B-162 can be factored:
1y%5E2%2B9y%2B-162+=+1%28y-9%29%2A%28y--18%29
Again, the answer is: 9, -18. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B-162+%29


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