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Question: Let a, b, c, d, e, f be nonnegative real numbers. 

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

 

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

 

The squares and same number of terms on each side makes me think we're supposed to use Cauchy to solve. However, I tried expanding parts A and B and the only thing i got were these large, nonsencial, unhelpful strings of terms.

 

Could someone please help me make these equations more Cauchy-friendly?

 Mar 31, 2020
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how about put 1 2 3 4 5 6 in a b c d e f 

this will work i think

dont direct add inside

do it step by step

then you will find the answer

 Apr 1, 2020
edited by Guest  Apr 1, 2020

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