xy=240, find x-y when x+y=32 and xy can some one provide the solution

Question

xy=240, find x-y when x+y=32 and x>y can some one provide the solution

anonymous · Answer

The two conditions imply$$\frac{ 240 }{ x } = 32 - x$$
$$x \in [ 12, 20 ] => (x,y) \in [ (12, 20), (20,12) ]$$

anonymous · Answer

thanks for taking time to respond, can you please explain as I did not quite understand

anonymous · Answer

Solve xy = 240 for y to get $$y = \frac{ 240 }{ x }$$
Solve x + y = 32 for y to get $$y = 32 - x$$
Put these together to get the expression that contains only 'x', as in my first response.
Simplify it to get $$240 = x ( 32 - x ) = 32x - x ^{2}$$
Rearrange this to get a quadratic equation in standard form.$$x ^{2} - 32x + 240 = 0$$
Solve this to obtain two values for 'x'. For each of these values of 'x' use one of the expressions for'y' to obtain the corresponding value for 'y'.
Now choose the (x,y) pair where x>y.