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Áp dụng BĐT Cauchy cho 4 số dương:
\(a^4+b^4+c^4+d^4\ge4\sqrt[4]{\left(abcd\right)^4}=4abcd\)
(Dấu "="\(\Leftrightarrow a=b=c=d\))
\(\Rightarrow a=b=c=d=\frac{2016}{4}=504\)
Bài này em làm nhầm rồi nhé: chú ý: \(\sqrt[4]{\left(abcd\right)^4}=\left|abcd\right|\ne abcd\) nhé!
\(\left(a+b+c\right)^2=2016^2\Leftrightarrow a^2+b^2+c^2+2\left(ab+cb+ca\right)=2016^2\)
\(\Leftrightarrow A=a^2+b^2+c^2=2016^2-2\left(ab+cb+ca\right)\) chia hết cho 2
=> A là 1 số chẵn
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Ta có
(m+n+p)^q >= m^q+n^q+p^q
=>a+b+c=1
=>(a+b+c)^2016=1 >= a2016 + b2016 + c2016
Mà a2016 + b2016 + c2016 >=0
=> a2016 + b2016 + c2016=1