Thread: Inequality very hard

Let $a,b,c,d\in \mathbb{R}$ and $\left\{\begin{matrix}
0<a\leq b\leq c\leq d\\
\frac{1}{a}+\frac{2}{b}+\frac{d}{c}\geq 3\\
\frac{2}{b}+\frac{d}{c}\geq 2
\end{matrix}\right.$. Prove that:
$$a^4+b^4+c^4-d^4\leq 17$$

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