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Let   \(a,b,c,d,e,f \)  be nonnegative real numbers.

(a) Prove that \((a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) \ge (ace + bdf)^4.\)

(b) Prove that \((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2\)
 

 May 16, 2020
 #1
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It's easy!  Just appy Markus's inequality.

 May 16, 2020
 #2
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I haven't learned that yet, could you please help me with the problem?

littlemixfan  May 16, 2020
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I have not managed to prove it algebraically but here is a graphical demonstration where it certainly appears to be true.

 

https://www.desmos.com/calculator/djm2pyxgsh

 

this is part a)

 May 17, 2020
edited by Melody  May 17, 2020
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thanks! ill take a look at it!

littlemixfan  May 17, 2020

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