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Mathematics
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MathMagician
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9
Maximize $(1-a)(1-c)+(1-b)(1-d)$ over $a^2+b^2=c^2+d^2=1$. [closed]
Feb 18, 2023
4
$f(x)$ and $g(x)$ are monic cubic polynomials, with $f(x)-g(x)=r$. If $f$ has roots $r+1$ and $r+7$, and $g$ has roots $r+3$ and $r+9$, then find $r$.
Mar 4, 2022
3
Closed form of $a_1=x$, $a_n=\left\lfloor\dfrac{(n+2)a_{n-1}-2}{n}\right\rfloor,n\ge 2$
Jul 13, 2023
3
Find $b_{32}$ if $\prod_{n=1}^{32}(1-z^n)^{b_n}\equiv 1-2z \pmod{z^{33}}$ and $b_n\in\mathbb{Z}^{+}$
May 4, 2022
3
Weird Problem on Polynomial Roots
Feb 27, 2022
3
Range of $\sqrt{a^2 + (1 - b)^2} + \sqrt{b^2 + (1 - c)^2} + \sqrt{c^2 + (1 - d)^2} + \sqrt{d^2 + (1 - a)^2}$ on $0 \le a,$ $b,$ $c,$ $d \le 1.$
Apr 5, 2022
3
A cube is dropped on the floor, and the triangular hole created has sides of lengths $68,$ $75,$ and $77.$ Find the depth of the hole.
Mar 11, 2022
2
$f(f(x - y)) = f(x) f(y) - f(x) + f(y) - xy$
Feb 17, 2022
2
Minimize $\displaystyle\sum_{1 \le i < j \le 95} a_i a_j$.
Feb 24, 2022
2
Weird Maximization Problem
Feb 26, 2022