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Buna!
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(Tiparita in graba, eventual am gresit la calcule, dar in principiu asa se rezolva astfel de sisteme.)
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df (gauss)
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Dupa o zi lunga de lucru, ajuns acasa am dat drumul la calculator ca sa verific existenta acelui zero macar, da, e bine:
(Code sage)
sage: var( 'a,b,c' );
sage: eq1 = ( a + b + c == 12 );
sage: eq2 = ( a^2 + b^2 + c^2 == 56 );
sage: eq3 = ( a^3 + b^3 + c^3 == 144 );
sage:
sage: solutii = solve( [ eq1, eq2, eq3 ], a,b,c );
sage: for solutie in solutii:
....: print solutie
....:
[a == 0, b == 2*I*sqrt(2) + 6, c == -2*I*sqrt(2) + 6]
[a == 0, b == -2*I*sqrt(2) + 6, c == 2*I*sqrt(2) + 6]
[a == 2*I*sqrt(2) + 6, b == -2*I*sqrt(2) + 6, c == 0]
[a == 2*I*sqrt(2) + 6, b == 0, c == -2*I*sqrt(2) + 6]
[a == -2*I*sqrt(2) + 6, b == 2*I*sqrt(2) + 6, c == 0]
[a == -2*I*sqrt(2) + 6, b == 0, c == 2*I*sqrt(2) + 6]
sage:
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df (gauss)
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