Michael Rozenberg

 98 Show that $(2,0,4) , (4,1,-1) , (6,7,7)$ form a right triangle 60 Why does the discriminant in the Quadratic Formula reveal the number of real solutions? 54 How to simplify $\int{\sqrt[4]{1-8{{x}^{2}}+8{{x}^{4}}-4x\sqrt{{{x}^{2}}-1}+8{{x}^{3}}\sqrt{{{x}^{2}}-1}}dx}$? 50 Can the product of three complex numbers ever be real? 41 Can sum of a rational number and its reciprocal be an integer?

### Reputation (174,994)

 -4 Inequality. $\sqrt{3+\frac{1}{a^2}}+\sqrt{3+\frac{1}{b^2}}+\sqrt{3+\frac{1}{c^2}} \geq 9.$ -2 Inequality. $\sqrt{3+\frac{1}{a^2}}+\sqrt{3+\frac{1}{b^2}}+\sqrt{3+\frac{1}{c^2}} \geq 9.$ -2 Inequality. $\sqrt{3+\frac{1}{a^2}}+\sqrt{3+\frac{1}{b^2}}+\sqrt{3+\frac{1}{c^2}} \geq 9.$ +6 Find maximize of $P=\frac{x\sqrt{yz}}{\sqrt{x^2+1}\sqrt[4]{\left(y^2+4\right)\left(z^2+9\right)}}$

### Questions (116)

 81 If $a+b=1$ so $a^{4b^2}+b^{4a^2}\leq1$ 40 Prove that $a\sqrt{a^2+bc}+b\sqrt{b^2+ac}+c\sqrt{c^2+ab}\geq\sqrt{2(a^2+b^2+c^2)(ab+ac+bc)}$ 32 Inequality $\sum\limits_{cyc}\frac{a^3}{13a^2+5b^2}\geq\frac{a+b+c}{18}$ 29 Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$ 26 Inequality with five variables

### Tags (435)

 5k inequality × 3247 1k contest-math × 691 3k algebra-precalculus × 1271 1k polynomials × 667 2k a.m.-g.m.-inequality × 793 1k cauchy-schwarz-inequality × 650 2k trigonometry × 816 1k real-analysis × 550 2k calculus × 792 1k geometry × 882

### Bookmarks (772)

 92 Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing 81 If $a+b=1$ so $a^{4b^2}+b^{4a^2}\leq1$ 81 References for multivariable calculus 73 Cardinality of set of real continuous functions 67 Examples of finite nonabelian groups.