Intereting Posts

How to effectively study math?
Is a maximal open simply connected subset $U$ of a manifold $M$, necessarily dense?
Drawing a tetrahedron from a parellelepiped to convince myself it is 1/6th the volume,
PDE $(\partial_{tt}+a\partial_t-b\nabla^2)f(r,t)=0$
Equation of a plane containing a point and perpendicular to a line
Apéry's constant ($\zeta(3)$) value
Is there a field extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?
Characterization of Harmonic Functions on the Punctured Disk
Are all numbers real numbers?
For any integer n greater than 1, $4^n+n^4$ is never a prime number.
Are there open problems in Linear Algebra?
Existence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$
Polarization: etymology question
When does a SES of vector bundles split?
How did Newton and Leibniz actually do calculus?

let $x,y,z>0$ such that $x^2+y^2+z^2=1$. Find the minimum of $$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$$

Is the answer $3\sqrt{3}$ by any chance?

- If $N=q^k n^2$ is an odd perfect number and $q = k$, why does this bound not imply $q > 5$?
- Proving the Schwarz Inequality for Complex Numbers using Induction
- Series and integrals for inequalities and approximations to $\log(n)$
- Symbol/notation/strategy for figuring out an unknown inequality?
- Does this inequality have any solutions in $\mathbb{N}$?
- Simple AM-GM inequality

- Inequality:$ (a^{2}+c^{2})(a^{2}+d^{2})(b^{2}+c^{2})(b^{2}+d^{2})\leq 25$
- Which of the numbers is larger: $7^{94}$ or $9^{91} $?
- Prove that $\phi(n) \geq \sqrt{n}/2$
- Hölder's inequality with three functions
- Proving by induction that $2^n \le 2^{n+1}-2^{n-1} - 1$ . Does my proof make sense?
- Prove $\sqrt{x^2+yz+2}+\sqrt{y^2+zx+2}+\sqrt{z^2+xy+2}\ge 6$, given $x+y+z=3$ and $x,y,z\ge0$
- $a,b,c$ are positive reals and distinct with $a^2+b^2 -ab=c^2$. Prove $(a-c)(b-c)<0$
- Suppose $(s_n)$ converges and that $s_n \geq a$ for all but finitely many terms, show $\lim s_n \geq a$
- Cauchy-Schwarz inequality and three-letter identities (exercise 1.4 from “The Cauchy-Schwarz Master Class”)
- How would you prove $\sum_{i=1}^{n} (3/4^i) < 1$ by induction?

Apply AM-GM and CS inequalities:$$\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z} \geq \dfrac{9}{x+y+z} \geq \dfrac{9}{\sqrt{3}\cdot (x^2+y^2+z^2)}= 3\sqrt{3}$$

Just another way, sum three AM-GMs of form:

$$\frac1x + \frac1x +3\sqrt{3}x^2 \ge 3\sqrt3 $$

Equality is iff $x = \frac1{\sqrt3} = y= z$

- Are there irreducible polynomials that are partially solvable by radicals?
- Can a number with $100$ $0$'s $100$ $1$'s and $100$ $2$'s ever be a perfect square?
- A closed form of $\sum_{k=0}^\infty\frac{(-1)^{k+1}}{k!}\Gamma^2\left(\frac{k}{2}\right)$
- Prove the following trigonometric identity.
- Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
- If $(a_n)$ is such that $\sum_{n=1}^\infty a_nb_n$ converges for every $b\in\ell_2$, then $a\in\ell_2$
- what is the degree of $f :S^n \to S^n$ when $f$ has no fixed points?
- For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
- Is there a way to evaluate the derivative of $x$! without using Gamma function?
- Finding conjugacy classes of $PGL_{2}(\mathbb{F}_{q})$
- Hypersurfaces containing given lines
- How can I show that the polynomial $p = x^5 – x^3 – 2x^2 – 2x – 1$ is irreducible over $\Bbb Q$?
- Are there any commutative rings in which no nonzero prime ideal is finitely generated?
- Dimension of Range and Null Space of Composition of Two Linear Maps
- Upper bound on cardinality of a field