Question

Prove that $\sum_{cyc}\sqrt{a^2+\frac{1}{\left(b+1\right)^2}}\ge \frac{\sqrt{181}}{5}$

score 321 · Answer 1 · 2026-03-26 11:00:53

321

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Prove that $\sum_{cyc}\sqrt{a^2+\frac{1}{\left(b+1\right)^2}}\ge \frac{\sqrt{181}}{5}$

Published on 26 Mar 2026 - 11:00

score 960 · Answer 2 · 2026-04-12 14:27:32

960

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Calculate: $\sin9°$

Published on 12 Apr 2026 - 14:27

score 2k · Answer 3 · 2017-06-07 14:07:52

2k

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Solve the equation $\sqrt{5x^2+4x}-\sqrt{x^2-3x-18}=5\sqrt{x}$

Published on 07 Jun 2017 - 14:07

score 3.4k · Answer 4 · 2017-06-08 17:12:26

3.4k

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Even-even-odd rule with multiple terms in the radicand

Published on 08 Jun 2017 - 17:12

score 289 · Answer 5 · 2017-06-10 08:01:08

289

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$A^{1\over A} = B^{1\over B} = C^{1\over 3} $ and $ A^{BC}+B^{AC}+C^{AB}=729 $ Find the value of $A^{1\over A}$

Published on 10 Jun 2017 - 8:01

score 2.4k · Answer 6 · 2026-03-25 14:25:59

2.4k

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Show which of $6-2\sqrt{3}$ and $3\sqrt{2}-2$ is greater without using calculator

Published on 25 Mar 2026 - 14:25

score 222 · Answer 7 · 2017-06-12 05:06:55

222

Views

Solve the equation $\sqrt[3]{x+2}+\sqrt[3]{2x-1}+x=4$

Published on 12 Jun 2017 - 5:06

score 494 · Answer 8 · 2017-06-13 07:25:19

494

Views

Help Solving $F_N = \frac{1}{\sqrt5}((\frac{1+\sqrt5}{2})^N - (\frac{1-\sqrt5}{2})^N)$ by Induction

Published on 13 Jun 2017 - 7:25

score 210 · Answer 9 · 2017-06-13 19:47:36

210

Views

Solve $(2^x+3^x+5^x)^3=160^x$

Published on 13 Jun 2017 - 19:47

score 92 · Answer 10 · 2026-03-27 12:13:01

92

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Quartic equation $ x^4-mx^2-4=0$ has root $\sqrt[4]{3-2\sqrt2}+\sqrt[4] {3+2\sqrt2}$. Find $m$

Published on 27 Mar 2026 - 12:13

score 413 · Answer 11 · 2017-06-16 17:29:37

413

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Which expression is equivalent to $\frac{\sqrt{3+x}}{\sqrt{3-x}}$ for all $x$ such that $-3 < x < 3$

Published on 16 Jun 2017 - 17:29

score 449 · Answer 12 · 2026-04-12 14:15:33

449

Views

Inequality with cyclic sum

Published on 12 Apr 2026 - 14:15

score 127 · Answer 13 · 2026-04-01 08:05:45

127

Views

Solve $x^2+y^2+\frac {2xy}{x+y}=1$, $\sqrt {x+y}=x^2-y$

Published on 01 Apr 2026 - 8:05

score 60 · Answer 14 · 2026-03-30 16:22:15

60

Views

Limit that is able to count a square root.

Published on 30 Mar 2026 - 16:22

score 108 · Answer 15 · 2017-06-20 04:34:30

108

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The function $f(x)=(1-\frac{\sqrt{21-4a-a^2}}{a+1})x^3+5x+\sqrt7$ is increasing at every point of its domain.

Published on 20 Jun 2017 - 4:34

List Question

Prove that $\sum_{cyc}\sqrt{a^2+\frac{1}{\left(b+1\right)^2}}\ge \frac{\sqrt{181}}{5}$

Calculate: $\sin9°$

Solve the equation $\sqrt{5x^2+4x}-\sqrt{x^2-3x-18}=5\sqrt{x}$

Even-even-odd rule with multiple terms in the radicand

$A^{1\over A} = B^{1\over B} = C^{1\over 3} $ and $ A^{BC}+B^{AC}+C^{AB}=729 $ Find the value of $A^{1\over A}$

Show which of $6-2\sqrt{3}$ and $3\sqrt{2}-2$ is greater without using calculator

Solve the equation $\sqrt[3]{x+2}+\sqrt[3]{2x-1}+x=4$

Help Solving $F_N = \frac{1}{\sqrt5}((\frac{1+\sqrt5}{2})^N - (\frac{1-\sqrt5}{2})^N)$ by Induction

Solve $(2^x+3^x+5^x)^3=160^x$

Quartic equation $ x^4-mx^2-4=0$ has root $\sqrt[4]{3-2\sqrt2}+\sqrt[4] {3+2\sqrt2}$. Find $m$

Which expression is equivalent to $\frac{\sqrt{3+x}}{\sqrt{3-x}}$ for all $x$ such that $-3 < x < 3$

Inequality with cyclic sum

Solve $x^2+y^2+\frac {2xy}{x+y}=1$, $\sqrt {x+y}=x^2-y$

Limit that is able to count a square root.

The function $f(x)=(1-\frac{\sqrt{21-4a-a^2}}{a+1})x^3+5x+\sqrt7$ is increasing at every point of its domain.

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