Question

Exam recall of $\alpha^3+\beta^3+\gamma^3=(\alpha+\beta+\gamma)^3-3(\alpha+\beta+\gamma)(\alpha\beta+\beta\gamma+\gamma\alpha)+3\alpha\beta\gamma$

score 108 · Answer 1 · 2019-08-27 20:23:52

Exam recall of $\alpha^3+\beta^3+\gamma^3=(\alpha+\beta+\gamma)^3-3(\alpha+\beta+\gamma)(\alpha\beta+\beta\gamma+\gamma\alpha)+3\alpha\beta\gamma$

score 2.9k · Answer 2 · 2019-09-01 21:13:15

2.9k

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Solving $ax^3+bx^2+cx+d=0$ using a substitution different from Vieta's?

Published on 01 Sep 2019 - 21:13

score 305 · Answer 3 · 2019-09-05 13:25:38

The polynomial $x^3 + 2ax^2 + (2a^2 + b)x + c$ has three (real and not necessairily distinct) roots and $b$ is one of them. Prove that $(ac)^2 \le 3$.

score 459 · Answer 4 · 2019-09-06 21:09:47

459

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Integral solutions of $a^{2} + a = b^{3} + b$

Published on 06 Sep 2019 - 21:09

score 78 · Answer 5 · 2019-09-10 07:07:12

78

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Published on 10 Sep 2019 - 7:07

score 1k · Answer 6 · 2019-09-10 18:32:42

1k

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Cubic diophantine equation with a prime $x^3 + y^3 + z^3 - 3xyz = p$.

Published on 10 Sep 2019 - 18:32

score 894 · Answer 7 · 2019-09-19 22:18:20

894

Views

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score 936 · Answer 8 · 2026-03-25 17:40:23

936

Views

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Published on 25 Mar 2026 - 17:40

score 49 · Answer 9 · 2019-09-21 07:11:36

49

Views

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score 30 · Answer 10 · 2019-09-23 19:24:40

30

Views

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score 104 · Answer 11 · 2019-09-25 12:15:55

104

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score 2.6k · Answer 12 · 2019-09-29 09:04:20

2.6k

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How to prove that $2x^3+6x+1=0$ has no integer solution?

Published on 29 Sep 2019 - 9:04

score 283 · Answer 13 · 2019-09-29 21:08:00

283

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Solving $2x^3-24x^2+23x+283=0$

Published on 29 Sep 2019 - 21:08

score 25.4k · Answer 14 · 2014-03-15 22:45:56

25.4k

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Published on 15 Mar 2014 - 22:45

score 167 · Answer 15 · 2014-03-24 11:15:31

167

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List Question

Exam recall of $\alpha^3+\beta^3+\gamma^3=(\alpha+\beta+\gamma)^3-3(\alpha+\beta+\gamma)(\alpha\beta+\beta\gamma+\gamma\alpha)+3\alpha\beta\gamma$

Solving $ax^3+bx^2+cx+d=0$ using a substitution different from Vieta's?

The polynomial $x^3 + 2ax^2 + (2a^2 + b)x + c$ has three (real and not necessairily distinct) roots and $b$ is one of them. Prove that $(ac)^2 \le 3$.

Integral solutions of $a^{2} + a = b^{3} + b$

Find conditions on $a$ and $b$ given that two cubics are the same.

Cubic diophantine equation with a prime $x^3 + y^3 + z^3 - 3xyz = p$.

Solving the cubic without complex numbers

Find a general formula for a tangent to a cubic which, is also normal to the cubic at the second intersection

Factoring a polynomial with complex roots

Calculate number of quadratic sequence progressions within a fixed value

Solving cube complex equation with z and i

How to prove that $2x^3+6x+1=0$ has no integer solution?

Solving $2x^3-24x^2+23x+283=0$

How to solve for a non-factorable cubic equation?

Solution for cubic algebra

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