Plz help me solve for x and y

x^3+y^3=1
x^4+y^4=1
help???

1 answer

clearly, x and y are non-negative. For, if x^3+y^3=1, then if x<0, y>1, and then x^4+y^4>1.

Other than (0,1) and (1,0) I cannot think of any real solutions.
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