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### Questions (243)

 25 Seems that I just proved $2=4$. 22 Strategies to denest nested radicals. 22 Show that $\sqrt[3]{2+\frac {10} 9\sqrt 3}+\sqrt[3]{2-\frac {10} 9\sqrt 3}=2$ 17 Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer. 16 Show that $\frac 1 {\sqrt{x+y}}+\frac 1 {\sqrt{y+z}}+\frac 1 {\sqrt{z+x}}\geq2+\frac 1 {\sqrt2}$.

### Reputation (6,030)

 +5 Find the maximum and minimum of $\cos x\sin y\cos z$. +65 What is the name of the circle that is tangent to three mutually-tangent circles centered at the vertices of a triangle? +5 Let $a,b$ be positive integers that are coprime, then $ac+1=bd$ for some positive integers $c,d$. +5 Can $x^2+y^2,y^2+z^2,z^2+x^2$ and $x^2+y^2+z^2$ all be square numbers?

 40 Why does $\tan^{-1}(1)+\tan^{-1}(2)+\tan^{-1}(3)=\pi$? 13 Show that $d/dx (a^x) = a^x\ln a$. 10 How to simplify an expression like this: $(x^2+x^{-2}-2)^{1/2}$ 8 Evaluating tetration to infinite heights (e.g., $2^{2^{2^{2^{.^{.^.}}}}}$) 6 $\frac{\mathrm d} {\mathrm dx}\sqrt{1/e^x}=$?

### Tags (110)

 50 trigonometry × 14 8 exponentiation × 2 33 algebra-precalculus × 35 8 recursion 32 calculus × 34 6 polynomials × 4 18 sequences-and-series × 21 6 roots × 3 9 integration × 13 5 inequality × 17

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 Mathematics 6,030 rep 31757 Stack Overflow 131 rep 7 TeX - LaTeX 121 rep 5 Chemistry 117 rep 5 Physics 114 rep 4