Skip to main content
Iuli's user avatar
Iuli's user avatar
Iuli's user avatar
Iuli
  • Member for 11 years, 11 months
  • Last seen more than a month ago
  • Timisoara, Romania
45 votes

How can I prove that $xy\leq x^2+y^2$?

12 votes
Accepted

Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$

11 votes

How to calculate square matrix to power n?

10 votes

Is $|1-i|$ larger than $|1|$?

10 votes
Accepted

How may I prove this inequality?

10 votes
Accepted

Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$

7 votes

$\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\geq \frac{3}{\sqrt{2}}$

7 votes

$\lim\limits_{n\to\infty} \frac{n}{\sqrt[n]{n!}} =e$

7 votes

How do you find the limit of $\lim_{x \to 0} \frac{1-e^{6x}}{1-e^{3x}}$

6 votes

Inequality. $\sum{\sqrt{x^2+xy+y^2}}\geq \sum{\sqrt{2x^2+xy}}.$

5 votes

Inequality. $\frac{1}{16}(a+b+c+d)^3 \geq abc+bcd+cda+dab$

5 votes
Accepted

Limits and continuity problem

5 votes

How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?

4 votes

Proving a Complex Number is Real

4 votes
Accepted

Inequality. $\frac{a^3}{a+b}+\frac{b^3}{b+c}+\frac{c^3}{c+a} \geq \frac{ab+bc+ca}{2}$

4 votes

Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{9}{a+b+c} : (a, b, c) > 0$

4 votes
Accepted

Inequality. $ab^2+bc^2+ca^2 \geq a+b+c.$

3 votes

What are the math challenges websites?

3 votes
Accepted

Inequality. $\frac{1}{\sqrt{x^2+yz+3}}+\frac{1}{\sqrt{y^2+zx+3}}+\frac{1}{\sqrt{z^2+xy+3}} \geq 1$

3 votes

Inequality: $(a^3+a+1)(b^3+b+1)(c^3+c+1) \leq 27$

3 votes

Why does $\frac{|x|}{x^2}$ reduce to $\frac{1}{|x|}$?

3 votes

Identify a formula for each entry of the matrix $\small \begin{pmatrix} 1 & 3 \\ 2 & 6 \end{pmatrix}^n$

3 votes
Accepted

Solve this Trigonometric equation

2 votes

Proving $4^{47}\equiv 4\pmod{12}$

2 votes

Show that $\sum^{n}_{k=1}(k+2)(k+4) = \frac{2n^{3} + 21n^{2} + 67n}{6}$

2 votes

Find the following limit problem

2 votes

Show that determinant of a symmetric matrix of order $4$ is $0$

2 votes

Inequality $\sum_{cyc}\frac{(a+b)^{3}}{\sqrt[3]{2(a+b)(a^{2}+b^{2})}}\ge{12}$ when $ab+bc+ca=6$

2 votes
Accepted

Simultaneous Equations and Vectors

2 votes

Summation of $i \cdot j$ from $ 1$ to$ 3$