cho a,b,c,d dương và a+b+c+d=1

N

noinhobinhyen

Ta có

(4a+1+4b+1+4c+1+4d+1)24(4a+4b+4c+4d+4)=32(\sqrt{4a+1}+\sqrt{4b+1}+\sqrt{4c+1}+\sqrt{4d+1})^2 \leq 4(4a+4b+4c+4d+4)=32

4a+1+4b+1+4c+1+4d+142\Rightarrow \sqrt{4a+1}+\sqrt{4b+1}+\sqrt{4c+1}+\sqrt{4d+1} \leq 4\sqrt{2}
 
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