Question 43
Find the smallest number $k$ such that for all real numbers $x$, $y$ and $z$
$$
\left(x^{2}+y^{2}+z^{2}\right)^{2} \leq k\left(x^{4}+y^{4}+z^{4}\right)
$$
$$
\left(x^{2}+y^{2}+z^{2}\right)^{2} \leq k\left(x^{4}+y^{4}+z^{4}\right)
$$
MathNet 2016-part-03 — 184 problems (EN–VI) Question 43
Math Olympiad Vault · MathNet 2016-part-03 — 184 problems (EN–VI)