Question 894317
Two numbers, x and y.

{{{x^2+y^2=256}}} and {{{(x+y)^2=784}}}


The 784 equation is {{{x^2+y^2+2xy=784}}};  subtract the circle 256 equation from it:
{{{2xy=784-256}}}
{{{2xy=528}}}
{{{highlight_green(xy=264)}}}----THE ACTUAL ANSWER TO THE QUESTION
{{{y=264/x}}}, and try substituting this into the circle equation.


{{{x^2+(264/x)^2=256}}}
{{{x^4+264=256x^2}}}
{{{x^4-256x^2+264=0}}}
Solve for {{{x^2}}}
Discriminant:  {{{256^2-4*264=64480}}}
which is {{{2^5*5*13*31}}}
{{{x^2=(256+- 4sqrt(4030))/2}}}
{{{highlight(x=0+- ((256+- 4sqrt(4030))/2))}}}, which is four different values.


This is not really finished.
Still want to find y for each of those x values.


Note, the actual question was to find the product of x and y, which was actually found early in this work.
{{{highlight(xy=264)}}}.