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E

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$P \ge \sqrt{(4+4)^2+(a^2+4b^2)^2}$

GT \Leftrightarrow $a+ab+2b=\dfrac{5}{2}$

Ta có: $a^2+4b^2 \ge 4ab$

$2a^2+2 \ge 4a$

$8b^2+2\ge 8b$

\Rightarrow $3(a^2+4b^2) \ge 4(a+ab+2b)=10$

\Rightarrow $P \ge ...$
 
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