Question

Simplifying $a = \dfrac{\sqrt{x}}{x+3} $

score 89 · Answer 1 · 2026-03-30 02:10:38

89

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Simplifying $a = \dfrac{\sqrt{x}}{x+3} $

Published on 30 Mar 2026 - 2:10

score 47 · Answer 2 · 2020-06-05 01:23:58

47

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How to find rational solutions to a set of equations

Published on 05 Jun 2020 - 1:23

score 185 · Answer 3 · 2020-06-05 06:12:29

185

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Number of roots of the equation $x^{2016}-x^{2011}+x^{2006}-x^{2001}+1=0$

Published on 05 Jun 2020 - 6:12

score 128 · Answer 4 · 2026-04-02 17:32:40

128

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Find all x such that : $x^{x^{x^3({x^{x^{3}}+1)}+3}}=3^{81}$

Published on 02 Apr 2026 - 17:32

score 173 · Answer 5 · 2026-04-02 16:56:21

173

Views

Solve $\sqrt{x^2+8x+7}+\sqrt{x^2+3x+2}=\sqrt{6x^2+19x+13}$

Published on 02 Apr 2026 - 16:56

score 178 · Answer 6 · 2020-06-06 05:06:13

178

Views

Show that $p(x)=2x^6+12x^5+30x^4+60x^3+8x^2+30x+45$ has no real roots

Published on 06 Jun 2020 - 5:06

score 76 · Answer 7 · 2020-06-06 10:10:45

76

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If $\frac{t^2-x^2}{(t^2+x^2)^2}+\frac{(1-x)^2-t^2}{((1-x)^2+t^2)^2}=0$ for real $t$ and $0<x<1$, prove that $x=1/2$

Published on 06 Jun 2020 - 10:10

score 61 · Answer 8 · 2026-03-30 15:05:21

61

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How fast does the function $f(x) = \prod_{n=1}^\infty \sqrt[\displaystyle{2^n}]{x+2^{n-1}}$ grow in $x$?

Published on 30 Mar 2026 - 15:05

score 364 · Answer 9 · 2020-06-06 23:13:01

364

Views

Exactly one root of $p_n$ between two consecutive roots of $p_{n+1}$

Published on 06 Jun 2020 - 23:13

score 69 · Answer 10 · 2026-04-11 12:46:15

69

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existence of negative root

Published on 11 Apr 2026 - 12:46

score 82 · Answer 11 · 2020-06-07 08:47:56

82

Views

How do I find the product $(x_1^2+1)\dotsb(x_{2560}^2+1)$, given that the $x_j$ are roots of $x^{2560} + 2x^{2559} + \dotsb + 2561$?

Published on 07 Jun 2020 - 8:47

score 78 · Answer 12 · 2020-06-07 13:48:01

78

Views

Solve the equation $10x^2+11x+4=8(x+1)\sqrt{2x^2+x-1}$

Published on 07 Jun 2020 - 13:48

score 115 · Answer 13 · 2026-04-11 04:53:59

115

Views

Connection between Abel–Ruffini theorem and characteristic polynomial of matrices

Published on 11 Apr 2026 - 4:53

score 26 · Answer 14 · 2020-06-08 01:37:49

26

Views

The limit behavior of the positive root $η_1$ of power series $\sum_{k = - ν}^{+ ∞}{p_k t^k}$

Published on 08 Jun 2020 - 1:37

score 51 · Answer 15 · 2026-04-10 23:19:10

51

Views

Finding the proof of a bound on the roots of a polynomial

Published on 10 Apr 2026 - 23:19

List Question

Simplifying $a = \dfrac{\sqrt{x}}{x+3} $

How to find rational solutions to a set of equations

Number of roots of the equation $x^{2016}-x^{2011}+x^{2006}-x^{2001}+1=0$

Find all x such that : $x^{x^{x^3({x^{x^{3}}+1)}+3}}=3^{81}$

Solve $\sqrt{x^2+8x+7}+\sqrt{x^2+3x+2}=\sqrt{6x^2+19x+13}$

Show that $p(x)=2x^6+12x^5+30x^4+60x^3+8x^2+30x+45$ has no real roots

If $\frac{t^2-x^2}{(t^2+x^2)^2}+\frac{(1-x)^2-t^2}{((1-x)^2+t^2)^2}=0$ for real $t$ and $0<x<1$, prove that $x=1/2$

How fast does the function $f(x) = \prod_{n=1}^\infty \sqrt[\displaystyle{2^n}]{x+2^{n-1}}$ grow in $x$?

Exactly one root of $p_n$ between two consecutive roots of $p_{n+1}$

existence of negative root

How do I find the product $(x_1^2+1)\dotsb(x_{2560}^2+1)$, given that the $x_j$ are roots of $x^{2560} + 2x^{2559} + \dotsb + 2561$?

Solve the equation $10x^2+11x+4=8(x+1)\sqrt{2x^2+x-1}$

Connection between Abel–Ruffini theorem and characteristic polynomial of matrices

The limit behavior of the positive root $η_1$ of power series $\sum_{k = - ν}^{+ ∞}{p_k t^k}$

Finding the proof of a bound on the roots of a polynomial

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