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Mathematics
Dave Robin's user avatar
Dave Robin's user avatar
Dave Robin's user avatar
Dave Robin
  • Member for 4 years, 4 months
  • Last seen more than 3 years ago
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4
Given $a, b, c>0$, prove $\frac{a^4}{a+b}+\frac{b^4}{b+c}+\frac{c^4}{c+a}\geq \frac{1}{2}(a^{2}c+b^{2}a+c^{2}b)$
Apr 5, 2020
4
Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.
Apr 11, 2020
4
Prove that at least one real root of $ax^2+bx+c$ is in $(0;\sqrt{3}-1)$
Aug 9, 2020
2
Find the minimum value of $a^2+b^2+c^2+2abc$ when $a+b+c=3$ and $a,b,c\geq0$.
Apr 11, 2020
2
Find $\lim _{x\to +\infty }\left(2^{1-\left(\frac{1}{2}\right)^x}\right)$ without using logarithms.
Aug 10, 2020
2
How can I approximate $ \left(1+\frac{2}{4x-1}\right)^{x} $
Aug 14, 2020
1
Proving $\sum_{i=1}^{n} \frac{a_{i}^2+a_{i+1}a_{i+2}}{a_{i}(a_{i+1}+a_{i+2})} \geq n.$
Apr 3, 2020
1
Find the minimum value of $T=a^2+b^2+c^2+d^2$
Apr 4, 2020
1
Given $\cos C(\sin A +\sin B)=\sin C \cos(A-B)$, prove that triangle $ABC$ is equilateral.
Apr 11, 2020
0
Prove $x^{\frac{n(n-1)}{2}}y^{\frac{n(n-1)}{2}}(x^{n}+y^{n})\leq2$
Apr 3, 2020