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x^2 + y^2 + 2xy = 25 -> xy= 3, 2x^2y^2=18
x^2+y^2=19 -> (x^2+y^2)^2=361
x^4+y^4+2x^2y^2=361
x^4+y^4=361-18
x^4+y^4=343