Question

Solve the equation $x^2 + 4(\sqrt{1 - x} + \sqrt{1 + x}) - 8 = 0$

score 122 · Answer 1 · 2026-03-26 17:52:35

122

Views

Solve the equation $x^2 + 4(\sqrt{1 - x} + \sqrt{1 + x}) - 8 = 0$

Published on 26 Mar 2026 - 17:52

score 338 · Answer 2 · 2019-03-16 19:21:48

338

Views

Proof of Cauchy-Schwartz inequality with dot product and euclidean norm

Published on 16 Mar 2019 - 19:21

score 105 · Answer 3 · 2019-03-18 16:19:54

105

Views

($x,y,z$ are positive real numbers)

Published on 18 Mar 2019 - 16:19

score 162 · Answer 4 · 2026-03-25 09:28:40

162

Views

Prove that $\sum_{cyc}\frac{a}{a + b^4 + c^4} \le 1$ where $abc = 1$

Published on 25 Mar 2026 - 9:28

score 120 · Answer 5 · 2026-03-26 01:12:40

120

Views

Show this inequality $\frac{n}{a_1 - a_0} + \frac{n - 1}{a_2 - a_1} + \cdots + \frac{1}{a_n - a_{n-1}} \ge \sum_{k=1}^n \frac{k^2}{a_k}$

Published on 26 Mar 2026 - 1:12

score 108 · Answer 6 · 2026-03-25 09:28:56

108

Views

If $a+b+c=1$ and a,b,c ＞0 prove $\dfrac{b^2}{a+b^2}+\dfrac{c^2}{b+c^2}+\dfrac{a^2}{c+a^2} \geqslant \dfrac{3}{4}$

Published on 25 Mar 2026 - 9:28

score 96 · Answer 7 · 2026-03-26 12:06:32

96

Views

Prove that $\sum_{cyc}\frac{a^2}{ca^2 + 2c^2} \ge 1$

Published on 26 Mar 2026 - 12:06

score 622 · Answer 8 · 2019-03-28 04:54:52

622

Views

Show that $f_{n}(x)=\frac{x}{1+nx^{2}}$ converges uniformly.

Published on 28 Mar 2019 - 4:54

score 113 · Answer 9 · 2026-03-26 12:08:25

113

Views

Prove that $\frac{2-2a^2}{1+a^2}+\frac{1-b^2}{1+b^2}+\frac{1-c^2}{1+c^2} \leq \frac{9}{4}$

Published on 26 Mar 2026 - 12:08

score 2.9k · Answer 10 · 2019-03-31 21:07:14

2.9k

Views

Show that equality holds in the Cauchy-Schwarz inequality |⟨x, y⟩| ≤ ∥x∥ ∥y∥ . for x, y if and only if x and y are linearly dependent...

Published on 31 Mar 2019 - 21:07

score 335 · Answer 11 · 2019-04-02 17:30:18

335

Views

Confusing Cauchy-Schwarz Inequality Proof

Published on 02 Apr 2019 - 17:30

score 111 · Answer 12 · 2019-04-03 08:56:48

111

Views

How to show following inequality using the Cauchy-Schwarz Inequality?

Published on 03 Apr 2019 - 8:56

score 223 · Answer 13 · 2026-03-25 15:57:53

223

Views

A nice Nesbitt inequality from a strange inequality

Published on 25 Mar 2026 - 15:57

score 908 · Answer 14 · 2026-03-25 06:32:04

908

Views

Bounding integral of square root by square root of integral

Published on 25 Mar 2026 - 6:32

score 110 · Answer 15 · 2019-04-13 12:13:25

110

Views

What is that inequality - Cauchy-Schwarz for a single random variable?

Published on 13 Apr 2019 - 12:13

List Question

Solve the equation $x^2 + 4(\sqrt{1 - x} + \sqrt{1 + x}) - 8 = 0$

Proof of Cauchy-Schwartz inequality with dot product and euclidean norm

($x,y,z$ are positive real numbers)

Prove that $\sum_{cyc}\frac{a}{a + b^4 + c^4} \le 1$ where $abc = 1$

Show this inequality $\frac{n}{a_1 - a_0} + \frac{n - 1}{a_2 - a_1} + \cdots + \frac{1}{a_n - a_{n-1}} \ge \sum_{k=1}^n \frac{k^2}{a_k}$

If $a+b+c=1$ and a,b,c ＞0 prove $\dfrac{b^2}{a+b^2}+\dfrac{c^2}{b+c^2}+\dfrac{a^2}{c+a^2} \geqslant \dfrac{3}{4}$

Prove that $\sum_{cyc}\frac{a^2}{ca^2 + 2c^2} \ge 1$

Show that $f_{n}(x)=\frac{x}{1+nx^{2}}$ converges uniformly.

Prove that $\frac{2-2a^2}{1+a^2}+\frac{1-b^2}{1+b^2}+\frac{1-c^2}{1+c^2} \leq \frac{9}{4}$

Show that equality holds in the Cauchy-Schwarz inequality |⟨x, y⟩| ≤ ∥x∥ ∥y∥ . for x, y if and only if x and y are linearly dependent...

Confusing Cauchy-Schwarz Inequality Proof

How to show following inequality using the Cauchy-Schwarz Inequality?

A nice Nesbitt inequality from a strange inequality

Bounding integral of square root by square root of integral

What is that inequality - Cauchy-Schwarz for a single random variable?

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