Let x2+y2=u,xy=v.x^2+y^2=u, xy=v.x2+y2=u,xy=v. Then x4+x2y2+y4=(x2+y2)2−x2y2=u2−v2x^4+x^2y^2+y^4=(x^2+y^2)^2-x^2y^2=u^2-v^2x4+x2y2+y4=(x2+y2)2−x2y2=u2−v2
Hence
If x+y=5x+y=5x+y=5
If x+y=−5x+y=-5x+y=−5
Therefore
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