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A fifth degree equation in two variables: a clever solution

Question: Verify the identity: $latex (2xy+(x^{2}-2y^{2}))^{5}+(2xy-(x^{2}-2y^{2}))^{5}=(2xy+(x^{2}+2y^{2})i)^{5}+(2xy-(x^{2}+2y^{2})i)^{5}$ let us observe first that each of the fifth degree expre…