Mathematics
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tompi2394
  • Member for 1 year, 9 months
  • Last seen this week
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All Questions Answers
Score Newest
question
14
Let $x^3+\frac{1}{x^3}$ and $x^4+\frac{1}{x^4}$ are rational numbers. Show that $x+\frac{1}{x}$ is rational.
Aug 31, 2021
question
9
Find postive integer $x$ with $x>1$ and $\dfrac{x^6-1}{x-1}$ is perfect square
2 days ago
question
5
Let $a,b,c>0$ and $ab+bc+ca=3$. Prove that $abc(a+b)(b+c)(c+a)\leq8$
Jul 27
question
4
Prove $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{ab+bc+ca}{a^2+b^2+c^2}\ge4$
Jul 5
question
3
Prove $\left(\frac{u}{a}\right)^a.\left(\frac{v}{b}\right)^b.\left(\frac{w}{c}\right)^c \le \left(\frac{u+v+w}{a+b+c}\right)^{(a+b+c)} $ [duplicate]
Aug 28, 2021
question
2
Find minimum value of $\frac{x^3}{\sqrt{2(y^4+1)}}+\frac{y^3}{\sqrt{2(z^4+1)}}+\frac{z^3}{\sqrt{2(x^4+1)}}$
Aug 4, 2021
question
1
Prove a distance is a metric space
Jan 16, 2021
question
1
Find the prime numbers $p, q$ satisfying perfect square
Feb 9
question
0
$\frac{a}{(a+2b)^2}+\frac{b}{(b+2c)^2}+\frac{c}{(c+2a)^2}\ge\frac{1}{a+b+c}$ [duplicate]
Jul 29, 2021
question
0
An inequality with $a^3+b^3+c^3=a^4+b^4+c^4$
Nov 4, 2021

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