Question

Show that if a quadratic has rational coefficients and $x + y \sqrt{z}$ is a root, then $x - y \sqrt{z}$ must also be a root.

score 328 · Answer 1 · 2026-04-14 10:21:21

328

Views

Show that if a quadratic has rational coefficients and $x + y \sqrt{z}$ is a root, then $x - y \sqrt{z}$ must also be a root.

Published on 14 Apr 2026 - 10:21

score 90 · Answer 2 · 2026-04-17 09:30:24

90

Views

Is 'x=+1 or x=-1' $\iff$ '(x+1)(x-1)=0' correct?

Published on 17 Apr 2026 - 9:30

score 227 · Answer 3 · 2026-04-18 21:15:46

227

Views

Easy way to see that $(x^2 + 5x + 4)(x^2 + 5x + 6) - 48 = (x^2 + 5x + 12)(x^2 + 5x - 2)$?

Published on 18 Apr 2026 - 21:15

score 76 · Answer 4 · 2026-04-14 17:09:50

76

Views

Find rational $a,b$ with $a\ne b$ such that $x²-bx-\frac{a³-b³}{3b}=0$ has rational solutions

Published on 14 Apr 2026 - 17:09

score 342 · Answer 5 · 2026-04-17 06:25:48

342

Views

Find all $z$ such that $\sqrt{5z+5} - \sqrt{3 - 3z} - 2\sqrt{z} = 0$.

Published on 17 Apr 2026 - 6:25

score 181 · Answer 6 · 2026-04-11 03:13:14

181

Views

Lattice points on a hyperbola.

Published on 11 Apr 2026 - 3:13

score 147 · Answer 7 · 2026-04-17 04:40:02

147

Views

Find all real values of $x$ which satisfy $\sqrt{x^2 + 1} + x^2 + 1 = 90$.

Published on 17 Apr 2026 - 4:40

score 4.6k · Answer 8 · 2026-04-15 23:55:08

4.6k

Views

Looking for a function that approximates a parabola

Published on 15 Apr 2026 - 23:55

score 4.4k · Answer 9 · 2026-04-09 00:34:13

4.4k

Views

Understanding the term "double roots" of a quadratic equation

Published on 09 Apr 2026 - 0:34

score 111 · Answer 10 · 2026-04-14 17:44:14

111

Views

Does $\sqrt{1+\sqrt{2}}$ belong to $\mathbb{Q}(\sqrt{2})$?

Published on 14 Apr 2026 - 17:44

score 133 · Answer 11 · 2026-04-10 13:36:58

133

Views

Response surface and variables importance

Published on 10 Apr 2026 - 13:36

score 115 · Answer 12 · 2026-04-17 11:10:54

115

Views

Solve equation $xy^2-(3x^2-4x+1)y+x^3-2x^2+x=0$ , in $\mathbb R$

Published on 17 Apr 2026 - 11:10

score 200 · Answer 13 · 2026-04-15 14:50:37

Find every quadratic polynomial of the form $p(x)=x^2+bx+c$ such that if $r$ is a root then $r^2 − 4$ is also a root of $p(x)$.

score 131 · Answer 14 · 2026-04-16 16:30:55

131

Views

$\frac{2019(x^{4}+2)}{x^{2}y+1} \in \mathbb{N^*}$

Published on 16 Apr 2026 - 16:30

score 611 · Answer 15 · 2026-04-11 05:25:04

611

Views

Finding a non-linear equation from a set of points

Published on 11 Apr 2026 - 5:25

List Question

Show that if a quadratic has rational coefficients and $x + y \sqrt{z}$ is a root, then $x - y \sqrt{z}$ must also be a root.

Is 'x=+1 or x=-1' $\iff$ '(x+1)(x-1)=0' correct?

Easy way to see that $(x^2 + 5x + 4)(x^2 + 5x + 6) - 48 = (x^2 + 5x + 12)(x^2 + 5x - 2)$?

Find rational $a,b$ with $a\ne b$ such that $x²-bx-\frac{a³-b³}{3b}=0$ has rational solutions

Find all $z$ such that $\sqrt{5z+5} - \sqrt{3 - 3z} - 2\sqrt{z} = 0$.

Lattice points on a hyperbola.

Find all real values of $x$ which satisfy $\sqrt{x^2 + 1} + x^2 + 1 = 90$.

Looking for a function that approximates a parabola

Understanding the term "double roots" of a quadratic equation

Does $\sqrt{1+\sqrt{2}}$ belong to $\mathbb{Q}(\sqrt{2})$?

Response surface and variables importance

Solve equation $xy^2-(3x^2-4x+1)y+x^3-2x^2+x=0$ , in $\mathbb R$

Find every quadratic polynomial of the form $p(x)=x^2+bx+c$ such that if $r$ is a root then $r^2 − 4$ is also a root of $p(x)$.

$\frac{2019(x^{4}+2)}{x^{2}y+1} \in \mathbb{N^*}$

Finding a non-linear equation from a set of points

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