Question 1051119
<pre><b>
{{{system(

matrix(1,3,x^3,""="",20x + 7y) , matrix(1,3,y^3,""="",7x + 20y))}}}

Add the two equations:

{{{x^3+y^3}}}{{{""=""}}}{{{27x+27y}}}

Factor both sides:

{{{(x+y)(x^2-xy+y^2)}}}{{{""=""}}}{{{27(x+y)}}}

x and y do not have the same absolute values,
therefore (x+y) does not equal 0 and we may divide
both sides by it.

{{{x^2-xy+y^2=27}}}

------------------------------------------

{{{system(x^3 = 20x + 7y , y^3 = 7x + 20y)}}}

Subtract the two equations:

{{{x^3-y^3}}}{{{""=""}}}{{{13x-13y}}}

Factor both sides:

{{{(x-y)(x^2+xy+y^2)}}}{{{""=""}}}{{{13(x-y)}}}

x and y do not have the same absolute values,
therefore (x-y) does not equal 0 and we may divide
both sides by it.

{{{x^2+xy+y^2}}}{{{""=""}}}{{{13}}}

--------------------------

Now we have the two equations:

{{{x^2+xy+y^2}}}{{{""=""}}}{{{13}}}
{{{x^2-xy+y^2}}}{{{""=""}}}{{{27}}}

Subtract them and get

      {{{2xy}}}{{{""=""}}}{{{-14}}}

      {{{xy = -7}}}

Answer: -7

Edwin</pre></b>