Home Competitions JBMO-SL 2008 A1
If for the real numbers x , y , z , k x, y, z, k x , y , z , k x ≠ y ≠ z ≠ x x \neq y \neq z \neq x x = y = z = x x 3 + y 3 + k ( x 2 + y 2 ) = y 3 + z 3 + k ( y 2 + z 2 ) = z 3 + x 3 + k ( z 2 + x 2 ) = 2008 x^{3}+y^{3}+k\left(x^{2}+y^{2}\right)=y^{3}+z^{3}+k\left(y^{2}+z^{2}\right)=z^{3}+x^{3}+k\left(z^{2}+x^{2}\right)=2008 x 3 + y 3 + k ( x 2 + y 2 ) = y 3 + z 3 + k ( y 2 + z 2 ) = z 3 + x 3 + k ( z 2 + x 2 ) = 2008 x y z x y z x y z
Dataset text NuminaMath olympiads . Quoted with source.
Show the answer
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Add a solution
Locator jbmo-sl/2008/a1 · Tag HAMN03WZ98 · Edit this page on GitHub · Keys: j next, k previous