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Mathematics
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David399's user avatar
David399
  • Member for 1 year, 9 months
  • Last seen more than 1 year ago
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57
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29
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29
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14
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Top posts
7
Find all real functions that satisfy: $f(x+y) = (f(x))^2 + (f(y))^2$, $x$, $y$ $\in$ $\mathbb{R}$
Mar 6, 2023
7
Prove that the equation $x^4-4x^3-14x^2-4x+1=0$ has a root $x = \tan 9^\circ$
Mar 25, 2023
2
Let $x, y\in \mathbb{R}$, solve the following system: $\begin{cases}x^9+y^9=1\\x^{10}+y^{10}=1 \end{cases}$
May 18, 2023
1
Given any $a,b,c \geq 1$, prove that $a^2 + b^2 + c^2 \geq 2a\sqrt{b-1} + 2b\sqrt{c-1} + 2c\sqrt{a-1}$
Oct 16, 2022
1
Let $H$ be the orthocenter of a triangle $ABC$, prove that $HA+HB+HC=a\cot A+b\cot B+c\cot C$
May 21, 2023
0
Find the maximum value of $|b|+|c|$.
Mar 27, 2023
-1
Solve the equation: $\lfloor{x}\rfloor+\lfloor{2x}\rfloor=\frac{5x-1}{2}$
Oct 7, 2022