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 
<pre>
x<sup>2</sup> + y<sup>2</sup> = 18

and their product is 2. 

xy = 2

Solve the system:

x<sup>2</sup> + y<sup>2</sup> = 18
xy = 2

Solve the second for y

y = {{{2/x}}}

Substitute in the first:

x<sup>2</sup> + {{{(2/x)}}}<sup>2</sup> = 18

x<sup>2</sup> + {{{(4/x^2)}}} = 18

Multiply through by x<sup>2</sup>

x<sup>4</sup> + 4 = 18x²

x<sup>4</sup> - 18x<sup>2</sup> + 4 = 0

Solve that by the quadratic formula for x<sup>2</sup>
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.
</pre>
if their difference is 3, find the difference of their cubes.
<pre>
Since their difference is not 3, the problem is botched.  You
don't need to continue.  Point this error out to your teacher.

Edwin</pre>