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Why doesn't Sage evaluate to zero on its own found roots?

g(x) = x^4 - 6x^2 - 2sqrt(5)x + 2x + 1/2*sqrt(5) - 1/2 g(x).solve(x)

This gave, [x == -1/2sqrt(-2sqrt(5) + 10) - 1, x == 1/2sqrt(-2sqrt(5) + 10) - 1, x == -1/2sqrt(2sqrt(5) + 6) + 1, x == 1/2sqrt(2sqrt(5) + 6) + 1]

But then g(1/2sqrt(-2sqrt(5) + 10) -1 ).simplify() is not zero! (same for the other roots!)

What is going on!?

Why doesn't Sage evaluate to zero on its own found roots?

g(x) = x^4 - 6x^2 - 2sqrt(5)x + 2x + 1/2*sqrt(5) - 1/2 1/2

g(x).solve(x)

This gave, [x == -1/2sqrt(-2sqrt(5) + 10) - 1, x == 1/2sqrt(-2sqrt(5) + 10) - 1, x == -1/2sqrt(2sqrt(5) + 6) + 1, x == 1/2sqrt(2sqrt(5) + 6) + 1]

But then g(1/2sqrt(-2sqrt(5) + 10) -1 ).simplify() is not zero! (same for the other roots!)

What is going on!?

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No.3 Revision

Why doesn't Sage evaluate to zero on its own found roots?

g(x) = x^4 - 6x^2 6*x^2 - 2sqrt(5)x 2*sqrt(5)*x + 2x 2*x + 1/2*sqrt(5) - 1/2

1/2

g(x).solve(x)

g(x).solve(x)

This gave, gave,

[x == -1/2sqrt(-2sqrt(5) -1/2*sqrt(-2*sqrt(5) + 10) - 1, x == 1/2sqrt(-2sqrt(5) 1/2*sqrt(-2*sqrt(5) + 10) - 1, x == -1/2sqrt(2sqrt(5) -1/2*sqrt(2*sqrt(5) + 6) + 1, x == 1/2sqrt(2sqrt(5) 1/2*sqrt(2*sqrt(5) + 6) + 1]

1]

But then g(1/2sqrt(-2sqrt(5) g(1/2*sqrt(-2*sqrt(5) + 10) -1 ).simplify() ).simplify() is not zero! (same for the other roots!)

What is going on!?