Question

Simplify $(1-x)^3+2y^3-3(1-x)y^2=0$ to $-(x - 2 y - 1) (x + y - 1)^2 = 0$

score 74 · Answer 1 · 2026-03-27 01:47:49

74

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Simplify $(1-x)^3+2y^3-3(1-x)y^2=0$ to $-(x - 2 y - 1) (x + y - 1)^2 = 0$

Published on 27 Mar 2026 - 1:47

score 219 · Answer 2 · 2020-06-09 10:29:50

219

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How to get the summation of a quadratic sequence with O(1)

Published on 09 Jun 2020 - 10:29

score 58 · Answer 3 · 2020-06-09 13:22:36

58

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Finding relation between coefficients in a limit

Published on 09 Jun 2020 - 13:22

score 145 · Answer 4 · 2026-03-30 13:36:26

145

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Quadratic Function from the Taiwan IMO TST 2005

Published on 30 Mar 2026 - 13:36

score 109 · Answer 5 · 2020-06-09 17:09:25

109

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Complex number equation $x^2+x+(1-i)=0$

Published on 09 Jun 2020 - 17:09

score 508 · Answer 6 · 2020-06-09 18:04:04

508

Views

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Published on 09 Jun 2020 - 18:04

score 68 · Answer 7 · 2020-06-09 19:41:39

68

Views

I am having trouble with this question including concepts on number theory and quadratic equations.

Published on 09 Jun 2020 - 19:41

score 93 · Answer 8 · 2020-06-09 23:26:43

93

Views

Find succinct formula for a series of numbers

Published on 09 Jun 2020 - 23:26

score 81 · Answer 9 · 2026-04-02 08:37:05

81

Views

How do I prove that the sum of $x_1 + x_2$ and $x_1 \cdot x_2$ is rational?

Published on 02 Apr 2026 - 8:37

score 302 · Answer 10 · 2020-06-11 17:03:01

302

Views

How to solve $x^2+3x+17\equiv 0\pmod{315}$?

Published on 11 Jun 2020 - 17:03

score 67 · Answer 11 · 2020-06-14 01:33:01

Given polynomial $P(x) = x^2 + ax + b$ and that there only exists one $c$ such that $P^2(c) = c$. Calculate the minimum value of $a + b + c$.

score 337 · Answer 12 · 2020-06-14 05:08:47

337

Views

Integral roots in quadratic equation

Published on 14 Jun 2020 - 5:08

score 573 · Answer 13 · 2020-06-14 05:33:19

573

Views

Formula for first difference is not the derivative?

Published on 14 Jun 2020 - 5:33

score 186 · Answer 14 · 2020-06-14 08:50:16

186

Views

If $a$ and $c$ are odd primes and $ax^2+bx+c=0$ has rational roots, where $b\in I$, then prove that one root will be independent of $a$ and $b$.

Published on 14 Jun 2020 - 8:50

score 66 · Answer 15 · 2020-06-15 00:31:48

66

Views

Solving $xy+z=a$, $x+y=b$, $yz=c$. Is there a trick to avoid a cubic?

Published on 15 Jun 2020 - 0:31

List Question

Simplify $(1-x)^3+2y^3-3(1-x)y^2=0$ to $-(x - 2 y - 1) (x + y - 1)^2 = 0$

How to get the summation of a quadratic sequence with O(1)

Finding relation between coefficients in a limit

Quadratic Function from the Taiwan IMO TST 2005

Complex number equation $x^2+x+(1-i)=0$

A sequence of quadratic equations

I am having trouble with this question including concepts on number theory and quadratic equations.

Find succinct formula for a series of numbers

How do I prove that the sum of $x_1 + x_2$ and $x_1 \cdot x_2$ is rational?

How to solve $x^2+3x+17\equiv 0\pmod{315}$?

Given polynomial $P(x) = x^2 + ax + b$ and that there only exists one $c$ such that $P^2(c) = c$. Calculate the minimum value of $a + b + c$.

Integral roots in quadratic equation

Formula for first difference is not the derivative?

If $a$ and $c$ are odd primes and $ax^2+bx+c=0$ has rational roots, where $b\in I$, then prove that one root will be independent of $a$ and $b$.

Solving $xy+z=a$, $x+y=b$, $yz=c$. Is there a trick to avoid a cubic?

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