AoPS Wiki talk:Problem of the Day/August 2, 2011
Revision as of 04:00, 2 August 2011 by BoyosircuWem (talk | contribs) (Created page with "Let <math>X=x^3</math> and <math>Y=y^3</math>. Then <math>X=218+Y</math> and <math>(218+Y)^{2/3} = 24 + Y^{2/3}</math>. Hence, <cmath>218+y^3=(24+y^2)^3</cmath> <cmath>(y-5)(674...")
Let and . Then and . Hence, This quartic has two real roots; and by the cubic formula. Call this second root (which evaluates to about -3.01) . The two real solutions are therefore: and