New posts in algebra-precalculus

Error in simplifying $\frac{\tan x+\sec x-1}{\tan x-\sec x+1}$

How do you solve $x^2 = \left(\frac 12\right)^x $?

Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$

Given a cubic and quadratic share a root, prove $(ac-b^{2})(bd-c^{2})\geq 0$

How to factor quadratic $ax^2+bx+c$?

What does $\lg x$ mean? is it $\log_2 x$ or $\log_{10} x$ in binary trees

Inequality $(1+x_1)(1+x_2)\ldots(1+x_n)\left(\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}\right)\geq 2n^2.$

100 blank cards, minimize the EV

How do we solve $a \le b^{r}-r$ for $r$?

How do negative powers and fractional powers make sense? [duplicate]

Let $x$, $y$, $z$ be three positive reals such that $x+y+z=\sqrt{10+\sqrt{19}}$ and $\frac1x+\frac1y+\frac1z=\sqrt{10-\sqrt{19}}$ ...

How many different number are there in sequence $⌊n/1\rfloor$, $⌊n/2⌋, ⌊n/3⌋, ..., ⌊n/n]$?

Rationalization of $\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$

Find all pair of cubic equations

All are sides of obtuse triangles

Find the value of infinite product $(2\cos(\frac{\pi}{9})-1)(2\cos(\frac{\pi}{27})-1)\cdot\cdot\cdot(2\cos(\frac{\pi}{3^{n+1}})-1)\cdot\cdot\cdot$ [duplicate]

Find the value of $\frac{1+2x}{1+\sqrt{1+2x}}+\frac{1-2x}{1-\sqrt{1-2x}}$ for $x=\frac{\sqrt3}{4}$.

Interesting short Inequality

$ a+b+c=0,\ a^2+b^2+c^2=1$ implies $ a^4+b^4+c^4=\frac{1}{2}$

Bound on matrix product $\begin{bmatrix} 1+\frac{1}{n} & -1 \\ 1 & 0 \end{bmatrix}\cdots\begin{bmatrix} 1+\frac{1}{2} & -1 \\ 1 & 0 \end{bmatrix}$