Question

If the roots of the equation $ax^2-2bx+c=0$ are complex ,then find the number of real roots of the equation $4e^x+(a+c)^2(x^3+x)=4b^2x$.

score 279 · Answer 1 · 2026-03-26 21:10:32

279

Views

If the roots of the equation $ax^2-2bx+c=0$ are complex ,then find the number of real roots of the equation $4e^x+(a+c)^2(x^3+x)=4b^2x$.

Published on 26 Mar 2026 - 21:10

score 115 · Answer 2 · 2026-03-25 14:26:52

115

Views

How to solve $\frac{|x+2|}{x-1}>\frac{x+1}{2x+1}$?

Published on 25 Mar 2026 - 14:26

score 345 · Answer 3 · 2026-03-25 22:05:08

345

Views

Prove that $\frac{6(a^2 + b^2 + c^2)}{a + b + c} \geq \frac{(a + b)^2}{b + c} + \frac{(b + c)^2}{c + a} + \frac{(a + c)^2}{a + b}$

Published on 25 Mar 2026 - 22:05

score 2k · Answer 4 · 2026-03-25 09:21:29

2k

Views

When is the integral of a square less than the square of the integral?

Published on 25 Mar 2026 - 9:21

score 31 · Answer 5 · 2018-08-06 20:26:40

31

Views

Bounding a sinusoid of unity amplitude with third order harmonics?

Published on 06 Aug 2018 - 20:26

score 450 · Answer 6 · 2026-04-01 00:25:25

450

Views

Question on a Proof of the Divergence of Harmonic Series

Published on 01 Apr 2026 - 0:25

score 31 · Answer 7 · 2026-03-26 06:32:46

31

Views

About taking expectations of supremums

Published on 26 Mar 2026 - 6:32

score 110 · Answer 8 · 2026-04-02 01:57:59

110

Views

If $a$, $b$ and $c$ are positive then $\sum\limits_{cyc} \frac{a^{2}}{b^{2}+c^{2}+bc}\geq 1$

Published on 02 Apr 2026 - 1:57

score 155 · Answer 9 · 2026-03-25 16:03:04

155

Views

Prove that: $\sum\limits_{cyc} \frac{b+c}{a^{2}+bc}\leq \sum\limits_{cyc} \frac{1}{a}$

Published on 25 Mar 2026 - 16:03

score 81 · Answer 10 · 2026-03-25 01:40:03

81

Views

Generalization of $f\left(\frac{x_1 + x_2}{2}\right) < {f(x_1) + f(x_2) \over 2}$ for odd number of variables.

Published on 25 Mar 2026 - 1:40

score 1.6k · Answer 11 · 2026-03-25 00:02:54

1.6k

Views

Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

Published on 25 Mar 2026 - 0:02

score 210 · Answer 12 · 2026-04-03 16:06:34

210

Views

Prove that: $\sum\limits_{cyc}\frac{1}{(b+c)^2+a^2}\leq \frac{3}{5}$

Published on 03 Apr 2026 - 16:06

score 313 · Answer 13 · 2026-03-26 01:23:35

313

Views

Find the maximum of the value$(n^{n-1}-1)\sqrt[n]{a_{1}a_{2}\cdots a_{n}}+\sqrt[n]{\frac{a^n_{1}+a^n_{2}+\cdots+a^n_{n}}{n}}$

Published on 26 Mar 2026 - 1:23

score 104 · Answer 14 · 2026-03-30 08:53:00

104

Views

Max modulus Constrained Optimization

Published on 30 Mar 2026 - 8:53

score 199 · Answer 15 · 2026-04-05 15:53:17

199

Views

Inequality in natural numbers

Published on 05 Apr 2026 - 15:53

List Question

If the roots of the equation $ax^2-2bx+c=0$ are complex ,then find the number of real roots of the equation $4e^x+(a+c)^2(x^3+x)=4b^2x$.

How to solve $\frac{|x+2|}{x-1}>\frac{x+1}{2x+1}$?

Prove that $\frac{6(a^2 + b^2 + c^2)}{a + b + c} \geq \frac{(a + b)^2}{b + c} + \frac{(b + c)^2}{c + a} + \frac{(a + c)^2}{a + b}$

When is the integral of a square less than the square of the integral?

Bounding a sinusoid of unity amplitude with third order harmonics?

Question on a Proof of the Divergence of Harmonic Series

About taking expectations of supremums

If $a$, $b$ and $c$ are positive then $\sum\limits_{cyc} \frac{a^{2}}{b^{2}+c^{2}+bc}\geq 1$

Prove that: $\sum\limits_{cyc} \frac{b+c}{a^{2}+bc}\leq \sum\limits_{cyc} \frac{1}{a}$

Generalization of $f\left(\frac{x_1 + x_2}{2}\right) < {f(x_1) + f(x_2) \over 2}$ for odd number of variables.

Prove that: $xy\sqrt{z}+yz\sqrt{x}+zx\sqrt{y}\geq x+y+z$

Prove that: $\sum\limits_{cyc}\frac{1}{(b+c)^2+a^2}\leq \frac{3}{5}$

Find the maximum of the value$(n^{n-1}-1)\sqrt[n]{a_{1}a_{2}\cdots a_{n}}+\sqrt[n]{\frac{a^n_{1}+a^n_{2}+\cdots+a^n_{n}}{n}}$

Max modulus Constrained Optimization

Inequality in natural numbers

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