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The Cauchy-Schwarz inequality states $|\langle x,y \rangle |\leq ||x||\cdot ||y||.$ Use this tag for questions related to the CS inequality and its applications.

9 votes

How to prove that $1/ ((y+z) x^4) + 1/ ((z+x) y^4) + 1/ ((x+y) z^4) \geq 3/2$ for $x, y, z>0...

Is the "cauchy-schwarz-inequality" tag a guess or a hint? . . . At any rate, it turns out to be a good start. Let $$ R := \frac1{(y+z) x^4} + \frac1{(z+x) y^4} + \frac1{(x+y) z^4}. $$ We show $xyz = …
Noam D. Elkies's user avatar