Question

Given $x-\sqrt {\dfrac {8}{x}}=9$, what is $x-\sqrt{8x}$ equal to?

score 128 · Answer 1 · 2019-07-24 12:31:38

128

Views

Given $x-\sqrt {\dfrac {8}{x}}=9$, what is $x-\sqrt{8x}$ equal to?

Published on 24 Jul 2019 - 12:31

score 128 · Answer 2 · 2026-03-25 06:12:59

128

Views

$\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{xz^2}{y}\geq x^2+y^2+z^2$

Published on 25 Mar 2026 - 6:12

score 90 · Answer 3 · 2019-07-25 15:57:06

90

Views

Showing $\left(\frac{\sum a_{i}+1}{2}\right)^{2}\geq \sum a_{i}^{2}.$

Published on 25 Jul 2019 - 15:57

score 76 · Answer 4 · 2019-07-28 03:27:59

76

Views

$y = (x^3 + \frac{1}{x^3}) - 6(x^2 + \frac{1}{x^2}) + 3(x + \frac{1}{x})$ find min value

Published on 28 Jul 2019 - 3:27

score 1.7k · Answer 5 · 2019-08-01 20:38:00

1.7k

Views

Finding the area under the curve from a graph

Published on 01 Aug 2019 - 20:38

score 125 · Answer 6 · 2026-03-25 03:04:12

125

Views

$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}-3\geq k\left ( \frac{x^{2}+y^{2}+z^{2}}{xy+yz+zx}-1 \right )$

Published on 25 Mar 2026 - 3:04

score 87 · Answer 7 · 2019-08-02 19:37:18

87

Views

Question about derivative symbolization when substituting

Published on 02 Aug 2019 - 19:37

score 331 · Answer 8 · 2026-03-25 06:39:15

331

Views

Prove the inequality $\sum \limits_{k=1}^n \frac{k+1}{k} \cdot \sum \limits_{k=1}^n \frac{k}{k+1} \le \frac{9}{8}n^2$

Published on 25 Mar 2026 - 6:39

score 1.1k · Answer 9 · 2019-08-03 13:40:36

1.1k

Views

What are the number of solutions of $|\sqrt{2\sin^4 x+18\cos^2 x}-\sqrt{2\cos^4 x+18\sin^2 x}|=1?$

Published on 03 Aug 2019 - 13:40

score 139 · Answer 10 · 2026-03-26 04:32:31

139

Views

Find the maximum possible perimeter of a right triangle

Published on 26 Mar 2026 - 4:32

score 471 · Answer 11 · 2026-03-25 09:27:36

471

Views

It may be a strengthening form of mean inequality

Published on 25 Mar 2026 - 9:27

score 79 · Answer 12 · 2019-08-05 13:00:00

79

Views

Prove that $AA_1, BB_1,CC_1$ are concurrent at $O$ and $M,O,G$ are collinear.

Published on 05 Aug 2019 - 13:00

score 194 · Answer 13 · 2026-03-26 19:18:37

194

Views

Difficulty understanding Metamath definitions of proper substitution.

Published on 26 Mar 2026 - 19:18

score 77 · Answer 14 · 2026-03-25 03:22:12

77

Views

Prove that $(\sum_{i=1}^m (x_{i})^{p})^{q}\ge(\sum_{i=1}^m(x_{i})^{q})^{p}$ for all $x_i\in\mathbb R^+$ and $p,q\in\mathbb R^+$ such that $p \le q$

Published on 25 Mar 2026 - 3:22

score 140 · Answer 15 · 2026-03-25 07:45:37

140

Views

Maximizing $\frac{a^2+6b+1}{a^2+a}$, where $a=p+q+r=pqr$ and $ab=pq+qr+rp$ for positive reals $p$, $q$, $r$

Published on 25 Mar 2026 - 7:45

List Question

Given $x-\sqrt {\dfrac {8}{x}}=9$, what is $x-\sqrt{8x}$ equal to?

$\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{xz^2}{y}\geq x^2+y^2+z^2$

Showing $\left(\frac{\sum a_{i}+1}{2}\right)^{2}\geq \sum a_{i}^{2}.$

$y = (x^3 + \frac{1}{x^3}) - 6(x^2 + \frac{1}{x^2}) + 3(x + \frac{1}{x})$ find min value

Finding the area under the curve from a graph

$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}-3\geq k\left ( \frac{x^{2}+y^{2}+z^{2}}{xy+yz+zx}-1 \right )$

Question about derivative symbolization when substituting

Prove the inequality $\sum \limits_{k=1}^n \frac{k+1}{k} \cdot \sum \limits_{k=1}^n \frac{k}{k+1} \le \frac{9}{8}n^2$

What are the number of solutions of $|\sqrt{2\sin^4 x+18\cos^2 x}-\sqrt{2\cos^4 x+18\sin^2 x}|=1?$

Find the maximum possible perimeter of a right triangle

It may be a strengthening form of mean inequality

Prove that $AA_1, BB_1,CC_1$ are concurrent at $O$ and $M,O,G$ are collinear.

Difficulty understanding Metamath definitions of proper substitution.

Prove that $(\sum_{i=1}^m (x_{i})^{p})^{q}\ge(\sum_{i=1}^m(x_{i})^{q})^{p}$ for all $x_i\in\mathbb R^+$ and $p,q\in\mathbb R^+$ such that $p \le q$

Maximizing $\frac{a^2+6b+1}{a^2+a}$, where $a=p+q+r=pqr$ and $ab=pq+qr+rp$ for positive reals $p$, $q$, $r$

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