List questions from a-m-g-m-inequality

Published on 02 Sep 2017 - 5:47

11.7k

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If $a+b+c=6$ and $a,b,c$ belongs to positive reals $\mathbb{R}^+$; then find the minimum value of $\frac{1}{a}+\frac{4}{b}+\frac{9}{c}$ .

Published on 02 Sep 2017 - 7:09

467

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Prove that: $2pq\sum_{k=1}^{n} a_kb_k\leq p^2\sum_{k=1}^{n} {a_k}^{2}+q^2 \sum_{k=1}^{n} {b_k}^{2}$

Published on 04 Sep 2017 - 11:39

135

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How to prove the following using Cauchy Schwarz inequality.

Published on 06 Sep 2017 - 3:58

107

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Show that $x^6 - x^4 +2 >0$ for all $x$

Published on 06 Sep 2017 - 8:08

316

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Minimizing the multivariable function $f(x,y) = \frac{1}{xy} + x^2y$

Published on 06 Sep 2017 - 13:04

156

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High school quadratic inequality question

Published on 07 Sep 2017 - 1:28

90

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Find minimum value of $7(a^4+b^4+c^4)+\frac{ab+bc+ca}{a^2b+b^2c+c^2a}$

Published on 08 Sep 2017 - 16:05

427

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Find the extreme values of the function

Published on 08 Sep 2017 - 18:17

169

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for $abc = 1$ and $a \le b \le c$ prove that $(a+1)(c+1)>3$

Published on 09 Sep 2017 - 21:22

127

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Find maximize and minimize of $P=x+y$

Published on 25 Mar 2026 - 6:31

1.5k

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Solve the following nonlinear system of equations:$ xy+xz+yz=12 , xyz=2+x+y+z$

Published on 13 Sep 2017 - 3:28

218

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Prove this inequality $\sum_{cyc}\sqrt{\frac{a}{3b^2+1}}\ge \frac{3}{2}$

Published on 26 Mar 2026 - 17:34

106

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How robust is the AM-GM inequality?

Published on 17 Sep 2017 - 2:13

146

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Find minimum possible values of the leading coefficient of quadratic equation

Published on 17 Sep 2017 - 10:11

List Question

If $abcd=1$ then $a^4b+b^4c+c^4d+d^4a\geq a+b+c+d$

If $a+b+c=6$ and $a,b,c$ belongs to positive reals $\mathbb{R}^+$; then find the minimum value of $\frac{1}{a}+\frac{4}{b}+\frac{9}{c}$ .

Prove that: $2pq\sum_{k=1}^{n} a_kb_k\leq p^2\sum_{k=1}^{n} {a_k}^{2}+q^2 \sum_{k=1}^{n} {b_k}^{2}$

How to prove the following using Cauchy Schwarz inequality.

Show that $x^6 - x^4 +2 >0$ for all $x$

Minimizing the multivariable function $f(x,y) = \frac{1}{xy} + x^2y$

High school quadratic inequality question

Find minimum value of $7(a^4+b^4+c^4)+\frac{ab+bc+ca}{a^2b+b^2c+c^2a}$

Find the extreme values of the function

for $abc = 1$ and $a \le b \le c$ prove that $(a+1)(c+1)>3$

Find maximize and minimize of $P=x+y$

Solve the following nonlinear system of equations:$ xy+xz+yz=12 , xyz=2+x+y+z$

Prove this inequality $\sum_{cyc}\sqrt{\frac{a}{3b^2+1}}\ge \frac{3}{2}$

How robust is the AM-GM inequality?

Find minimum possible values of the leading coefficient of quadratic equation

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