let-n-N-solve-for-real-numbers-x-3n-y-2n-y-3n-x-2n-4-

Question Number 155154 by mathdanisur last updated on 26/Sep/21

let n \in N^{+} solve for real numbers :

x^{3 n} - y^{2 n} = y^{3 n} - x^{2 n} = 4

Answered by MJS_new last updated on 26/Sep/21

x^{3 n} - y^{2 n} = y^{3 n} - x^{2 n} \Rightarrow y = x

x^{3 n} - x^{2 n} - 4 = 0

(x^{n} - 2) (x^{2 n} + x^{n} + 2) = 0

\Rightarrow x = y = 2^{1 / n}

Commented by mathdanisur last updated on 26/Sep/21

Very nice, thank you my dear