0

Prove that $$\frac{1}{4}\left(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a}\right) \geq \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}, \forall a,b,c,d \gt 0 $$ thanks.

Lê Thành Đạt
  • 4,228
anhei ah
  • 17
  • 2
    Show please your attempts – Michael Rozenberg Jan 28 '20 at 02:53
  • 2
    Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – Macavity Jan 28 '20 at 04:02
  • A stronger one is https://math.stackexchange.com/questions/1829520/prove-this-by-inequality-with-four-variables-inequality/3300298#3300298 – River Li Jan 28 '20 at 06:36
  • @Macavity: You are right, I mixed-up $a^2+b^2+c^2+d^2$ and $a^4+b^4+c^4+d^4$. – Martin R Jan 28 '20 at 08:31
  • @Macavity: What about this one https://math.stackexchange.com/q/852070/42969? But the only answer seems to be (admittedly) incomplete. – Martin R Jan 28 '20 at 08:33
  • @Martin Indeed that’s a duplicate, though the answer as you say is unsatisfactory. – Macavity Jan 28 '20 at 08:36
  • I have provided an answer here: https://math.stackexchange.com/a/3566860/317854 – Andreas Mar 02 '20 at 18:20
  • @Andreas Nice. BW is powerful. Some months ago, I used the same BW (none 'standard') to solve some inequalities (although I did not post my solution). For example, https://math.stackexchange.com/questions/2079934/prove-that-sum-limits-cyc-fraca4b-geq-sum-limits-cyca325-prod-limit – River Li Mar 03 '20 at 01:23
  • @Andreas Did you solve the stronger one? – River Li Mar 03 '20 at 01:24
  • @Andreas If you are interested in my some posts about the OP, refer to: https://mathoverflow.net/questions/193753/this-inequality-why-cant-solve-it-by-now-only-four-variables-inequality/337243#337243, and https://artofproblemsolving.com/community/q1h366320p12199188 – River Li Mar 03 '20 at 01:51
  • @RiverLi Thanks for the links. I had seen the mathoverflow one (and commented) but will look at the other problems. – Andreas Mar 03 '20 at 07:57

0 Answers0