Question

Sum of Squares for $a^2+b^2+c^2+d^2+abcd+1\ge ab+bc+cd+da + ac+bd$

score 207 · Answer 1 · 2026-03-25 19:11:43

207

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Sum of Squares for $a^2+b^2+c^2+d^2+abcd+1\ge ab+bc+cd+da + ac+bd$

Published on 25 Mar 2026 - 19:11

score 137 · Answer 2 · 2026-03-25 19:12:06

137

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Proving $\frac{1}{16} \sum \frac{(b+c)(c+a)}{ab} +\frac{9}{4} \geq 4\sum \frac{ab}{(b+c)(c+a)}$

Published on 25 Mar 2026 - 19:12

score 202 · Answer 3 · 2020-06-10 11:00:50

202

Views

Prove the following: If $\lim(x_n) = x$ and if $x > 0$, then there exists a natural number $M$ such that $x_n > 0$ for all $n\ge M$.

Published on 10 Jun 2020 - 11:00

score 1.1k · Answer 4 · 2026-03-29 11:51:44

1.1k

Views

Floor function of a product

Published on 29 Mar 2026 - 11:51

score 1.2k · Answer 5 · 2020-06-10 22:50:45

1.2k

Views

If $f$ and $g$ are both continuous, then the functions $\max\{f,g\}$ and $\min\{f,g\}$ are also continuous

Published on 10 Jun 2020 - 22:50

score 116 · Answer 6 · 2020-06-11 12:39:42

116

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Solve the equation $\sqrt{x^{2}+ 8}- \sqrt{x^{2}+ 3}+ 2x^{3}- x- 2= 0$ .

Published on 11 Jun 2020 - 12:39

score 300 · Answer 7 · 2026-03-26 14:18:44

300

Views

(Proof-check) Alternative formula for the total variation

Published on 26 Mar 2026 - 14:18

score 95 · Answer 8 · 2026-03-26 13:46:37

95

Views

Show the set $\{(x,y) \in \mathbb{Z} \times \mathbb{Z} : 3x+y=4\}$ is a function from $\mathbb{Z}$ to $ \mathbb{Z}$.

Published on 26 Mar 2026 - 13:46

score 120 · Answer 9 · 2026-03-30 03:56:39

120

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If $a, b, c, d\in\mathbb R^+, $ then prove that $\displaystyle\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+a}+\frac{d-a}{a+b}\ge 0.$

Published on 30 Mar 2026 - 3:56

score 1.2k · Answer 10 · 2020-06-12 07:39:06

1.2k

Views

Radius of circle that touches 3 circles, which in turn touch each other

Published on 12 Jun 2020 - 7:39

score 636 · Answer 11 · 2026-03-25 18:57:29

636

Views

Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

Published on 25 Mar 2026 - 18:57

score 114 · Answer 12 · 2026-03-26 13:45:21

114

Views

Prove $f$ is bijective if and only if the inverse relation $f^{-1}$ is a function from $B$ to $A$.

Published on 26 Mar 2026 - 13:45

score 1.2k · Answer 13 · 2020-06-14 05:14:53

1.2k

Views

Let $T$ and $U$ be non-zero linear transformations from $V$ to $W$. If $R(T)\cap R(U) = \{0\}$, prove that $\{T,U\}$ is LI

Published on 14 Jun 2020 - 5:14

score 214 · Answer 14 · 2026-03-29 07:00:28

214

Views

Given a tetrahedron, whose sides are $AB=3,AC=4,BC=5,AD=6,BD=7,CD=8$ . Find the volume of the tetrahedral $ABCD$ .

Published on 29 Mar 2026 - 7:00

score 85 · Answer 15 · 2020-06-14 07:59:10

85

Views

second countable topological space and relative topology

Published on 14 Jun 2020 - 7:59

List Question

Sum of Squares for $a^2+b^2+c^2+d^2+abcd+1\ge ab+bc+cd+da + ac+bd$

Proving $\frac{1}{16} \sum \frac{(b+c)(c+a)}{ab} +\frac{9}{4} \geq 4\sum \frac{ab}{(b+c)(c+a)}$

Prove the following: If $\lim(x_n) = x$ and if $x > 0$, then there exists a natural number $M$ such that $x_n > 0$ for all $n\ge M$.

Floor function of a product

If $f$ and $g$ are both continuous, then the functions $\max\{f,g\}$ and $\min\{f,g\}$ are also continuous

Solve the equation $\sqrt{x^{2}+ 8}- \sqrt{x^{2}+ 3}+ 2x^{3}- x- 2= 0$ .

(Proof-check) Alternative formula for the total variation

Show the set $\{(x,y) \in \mathbb{Z} \times \mathbb{Z} : 3x+y=4\}$ is a function from $\mathbb{Z}$ to $ \mathbb{Z}$.

If $a, b, c, d\in\mathbb R^+, $ then prove that $\displaystyle\frac{a-b}{b+c}+\frac{b-c}{c+d}+\frac{c-d}{d+a}+\frac{d-a}{a+b}\ge 0.$

Radius of circle that touches 3 circles, which in turn touch each other

Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

Prove $f$ is bijective if and only if the inverse relation $f^{-1}$ is a function from $B$ to $A$.

Let $T$ and $U$ be non-zero linear transformations from $V$ to $W$. If $R(T)\cap R(U) = \{0\}$, prove that $\{T,U\}$ is LI

Given a tetrahedron, whose sides are $AB=3,AC=4,BC=5,AD=6,BD=7,CD=8$ . Find the volume of the tetrahedral $ABCD$ .

second countable topological space and relative topology

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