Question

How to solve the Diophantine equation $an^2+bn+c=x^2$

score 101 · Answer 1 · 2026-04-25 23:39:53

101

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How to solve the Diophantine equation $an^2+bn+c=x^2$

Published on 25 Apr 2026 - 23:39

score 229 · Answer 2 · 2026-04-16 02:00:27

229

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How to show this inequality $ a^{14}-a^{13}+a^8-a^5+a^2-a+1>0$

Published on 16 Apr 2026 - 2:00

score 64 · Answer 3 · 2026-04-12 06:19:51

64

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Confusion about the use of principal roots and their use in expressions

Published on 12 Apr 2026 - 6:19

score 94 · Answer 4 · 2026-04-15 23:20:19

94

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Find $a$ such that ${x_1}^2+{x_2}^2$ takes the minimal value where $x_1, x_2$ are solutions to $x^2-ax+(a-1)=0$ DO NOT USE CALCULUS

Published on 15 Apr 2026 - 23:20

score 247 · Answer 5 · 2026-04-14 22:41:14

247

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Solve the equation $\sin x+\cos x=k \sin x \cos x$ for real $x$, where $k$ is a real constant.

Published on 14 Apr 2026 - 22:41

score 39 · Answer 6 · 2026-04-13 14:01:46

39

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How can I assemble an equation from these guide points?

Published on 13 Apr 2026 - 14:01

score 28 · Answer 7 · 2026-04-16 09:23:51

28

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Let p(x) be a quadratic polynomial such that distinct reals a and b,. p(a)=a and p(b)=b then find the 4 roots of. p[p(x)]-x=0.

Published on 16 Apr 2026 - 9:23

score 112 · Answer 8 · 2026-04-15 23:35:13

112

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Can We Prove that the Area Within a Parabola is Always Less than the Area Not Above the Parabola?

Published on 15 Apr 2026 - 23:35

score 81 · Answer 9 · 2026-04-17 05:32:17

81

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Find $a^{b^{c}}$ given that $\frac{1}{2}{a^2}+b^{2}+c^{2}-bc-ac=2(b-1).$

Published on 17 Apr 2026 - 5:32

score 160 · Answer 10 · 2026-04-14 14:37:05

160

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Two quadratics with one root opposite to each other

Published on 14 Apr 2026 - 14:37

score 73 · Answer 11 · 2026-04-16 21:12:09

73

Views

Show that $|a|+\sqrt{a^2+|b|}\leq(1+\sqrt{2})|r_1|$ for the larger root $r_1$ of $x^2-2ax+b$

Published on 16 Apr 2026 - 21:12

score 66 · Answer 12 · 2026-04-16 01:45:47

66

Views

$(x - 1)^2-2|x-1|+|k-3|=0$: Distinct number of integer values of $x$?

Published on 16 Apr 2026 - 1:45

score 53 · Answer 13 · 2026-04-09 09:10:21

53

Views

Convert a formula to a quadratic formula.

Published on 09 Apr 2026 - 9:10

score 182 · Answer 14 · 2026-04-13 23:04:59

182

Views

$e^{|\sin x|}+e^{-|\sin x|}+4a=0$ will have exactly four different solution in $[0,2\pi]$

Published on 13 Apr 2026 - 23:04

score 169 · Answer 15 · 2026-04-09 04:49:26

169

Views

Solve equation for z.

Published on 09 Apr 2026 - 4:49

List Question

How to solve the Diophantine equation $an^2+bn+c=x^2$

How to show this inequality $ a^{14}-a^{13}+a^8-a^5+a^2-a+1>0$

Confusion about the use of principal roots and their use in expressions

Find $a$ such that ${x_1}^2+{x_2}^2$ takes the minimal value where $x_1, x_2$ are solutions to $x^2-ax+(a-1)=0$ DO NOT USE CALCULUS

Solve the equation $\sin x+\cos x=k \sin x \cos x$ for real $x$, where $k$ is a real constant.

How can I assemble an equation from these guide points?

Let p(x) be a quadratic polynomial such that distinct reals a and b,. p(a)=a and p(b)=b then find the 4 roots of. p[p(x)]-x=0.

Can We Prove that the Area Within a Parabola is Always Less than the Area Not Above the Parabola?

Find $a^{b^{c}}$ given that $\frac{1}{2}{a^2}+b^{2}+c^{2}-bc-ac=2(b-1).$

Two quadratics with one root opposite to each other

Show that $|a|+\sqrt{a^2+|b|}\leq(1+\sqrt{2})|r_1|$ for the larger root $r_1$ of $x^2-2ax+b$

$(x - 1)^2-2|x-1|+|k-3|=0$: Distinct number of integer values of $x$?

Convert a formula to a quadratic formula.

$e^{|\sin x|}+e^{-|\sin x|}+4a=0$ will have exactly four different solution in $[0,2\pi]$

Solve equation for z.

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