user2838619

### Questions (73)

 13 Solving $x_1+x_2=x_3^2, x_2+x_3=x_4^2, x_3+x_4=x_5^2,x_4+x_5=x_1^2, x_5+x_1=x_2^2$ in reals 9 How many $10$ digit number exists that sum of their digits is equal to $15$? 8 Prove two of $\frac{2}{a}+\frac{3}{b}+\frac{6}{c}\geq 6,\frac{2}{b}+\frac{3}{c}+\frac{6}{a}\geq 6,\frac{2}{c}+\frac{3}{a}+\frac{6}{b}\geq 6$ are True 8 prove $\frac {ab}{a+b} \geq \sum ^n_{i=1} \frac{a_ib_i}{a_i+b_i}$ 7 Solve $x+3y=4y^3,y+3z=4z^3 ,z+3x=4x^3$ in reals

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 8 Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$ 8 Prove $\frac{ab}{\sqrt{2c+a+b}}+\frac{bc}{\sqrt{2a+b+c}}+\frac{ca}{\sqrt{2b+c+a}}\le\sqrt\frac{2}{3}$ if $a+b+c=2$ 5 The maximum and minimum values of the expression 4 Prove $(x+y)(y+z)(z+x)\ge\frac{8}{3}(x+y+z)\sqrt[3]{x^2y^2z^2}$ 2 Solving logarthmic inequality

### Tags (39)

 26 inequality × 47 8 summation × 2 8 cauchy-schwarz-inequality × 4 8 symmetric-polynomials × 2 8 a.m.-g.m.-inequality × 3 8 tangent-line-method × 2 8 jensen-inequality × 2 6 trigonometry × 5 8 substitution × 2 5 geometry × 19

### Bookmarks (36)

 754 Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem) 221 Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer? 195 Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$ 155 How to prove Euler's formula: $e^{i\varphi}=\cos(\varphi) +i\sin(\varphi)$? 154 What's the point in being a “skeptical” learner [closed]

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