SOLUTION: I'm having a hard time making an equation for this problem. Please explain how to solve this: The sum of the squares of two numbers is 18 and their product is 2. if their differenc

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm having a hard time making an equation for this problem. Please explain how to solve this: The sum of the squares of two numbers is 18 and their product is 2. if their differenc      Log On


   

Question 775369: I'm having a hard time making an equation for this problem. Please explain how to solve this: The sum of the squares of two numbers is 18 and their product is 2. if their difference is 3, find the difference of their cubes.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I'm having a hard time making an equation for this problem. Please explain how to solve this: The sum of the squares of two numbers is 18 
x2 + y2 = 18

and their product is 2. 

xy = 2

Solve the system:

x2 + y2 = 18
xy = 2

Solve the second for y

y = 2%2Fx

Substitute in the first:

x2 + %282%2Fx%292 = 18

x2 + %284%2Fx%5E2%29 = 18

Multiply through by x2

x4 + 4 = 18x²

x4 - 18x2 + 4 = 0

Solve that by the quadratic formula for x2
and then take square roots you get

one of them is approximately 4.216 and the other is 
approximately 0.474, or they could be the negatives of those.

if their difference is 3, find the difference of their cubes.
Since their difference is not 3, the problem is botched.  You
don't need to continue.  Point this error out to your teacher.

Edwin