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New posts in algebra-precalculus
Error in simplifying $\frac{\tan x+\sec x-1}{\tan x-\sec x+1}$
algebra-precalculus
trigonometry
How do you solve $x^2 = \left(\frac 12\right)^x $?
algebra-precalculus
logarithms
exponentiation
Prove that $\tan^{-1}\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}=\frac{\pi}{4}+\frac 12 \cos^{-1}x^2$
algebra-precalculus
trigonometry
solution-verification
inverse-function
Given a cubic and quadratic share a root, prove $(ac-b^{2})(bd-c^{2})\geq 0$
real-analysis
algebra-precalculus
polynomials
roots
How to factor quadratic $ax^2+bx+c$?
algebra-precalculus
factoring
quadratics
What does $\lg x$ mean? is it $\log_2 x$ or $\log_{10} x$ in binary trees
algebra-precalculus
logarithms
definition
trees
Inequality $(1+x_1)(1+x_2)\ldots(1+x_n)\left(\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_n}\right)\geq 2n^2.$
algebra-precalculus
inequality
contest-math
100 blank cards, minimize the EV
probability
algebra-precalculus
How do we solve $a \le b^{r}-r$ for $r$?
algebra-precalculus
exponentiation
roots
How do negative powers and fractional powers make sense? [duplicate]
real-analysis
algebra-precalculus
exponentiation
Let $x$, $y$, $z$ be three positive reals such that $x+y+z=\sqrt{10+\sqrt{19}}$ and $\frac1x+\frac1y+\frac1z=\sqrt{10-\sqrt{19}}$ ...
algebra-precalculus
How many different number are there in sequence $⌊n/1\rfloor$, $⌊n/2⌋, ⌊n/3⌋, ..., ⌊n/n]$?
algebra-precalculus
Rationalization of $\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$
algebra-precalculus
fractions
radicals
rationalising-denominator
Find all pair of cubic equations
algebra-precalculus
quadratics
cubics
All are sides of obtuse triangles
algebra-precalculus
geometry
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]
algebra-precalculus
infinite-product
Find the value of $\frac{1+2x}{1+\sqrt{1+2x}}+\frac{1-2x}{1-\sqrt{1-2x}}$ for $x=\frac{\sqrt3}{4}$.
algebra-precalculus
roots
radicals
Interesting short Inequality
algebra-precalculus
inequality
polynomials
contest-math
real-numbers
$ a+b+c=0,\ a^2+b^2+c^2=1$ implies $ a^4+b^4+c^4=\frac{1}{2}$
algebra-precalculus
riemannian-geometry
convex-geometry
Bound on matrix product $\begin{bmatrix} 1+\frac{1}{n} & -1 \\ 1 & 0 \end{bmatrix}\cdots\begin{bmatrix} 1+\frac{1}{2} & -1 \\ 1 & 0 \end{bmatrix}$
sequences-and-series
matrices
algebra-precalculus
inequality
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