Question 1127779
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{{{x^2(x+y+1)}}} = {{{y^2(y+x+1)}}}  ====>


{{{x^2(x+y+1)}}} - {{{y^2(y+x+1)}}} = 0  ====>


{{{(x^2 - y^2)*(x + y + 1)}}} = 0  ====>


(x - y)*(x + y)*(x + y + 1) = 0  ====>


This equation codes 3 (three, THREE) straight lines.


    1.  One equation is the straight line y = x.


    2.  Second equation is the straight line  y = -x.


    3.  Third equation is the straight line  y = -x - 1.
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Solved.