[TOÁN 9] tìm cực trị

T

transformers123

$P=4x^2-x+\dfrac{3}{4x}+2012$

$\iff P=x^2-x+\dfrac{1}{4}+(3x^2+\dfrac{3}{8x}+\dfrac{3}{8x})+\dfrac{8047}{4}$

$\iff P \ge (x-\dfrac{1}{2})^2+3\sqrt[3]{3x^2.\dfrac{3}{8x}.\dfrac{3}
{8x}}+\dfrac{8047}{4}$

$\iff P \ge \dfrac{9}{4}+\dfrac{8047}{4}$

$\iff P \ge 2014$

Dấu "=" xảy ra khi $x=\dfrac{1}{2}$
 
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