Giải thích các bước giải:
Do đó:
$P=|a|+|b|$
$\to P=|-\dfrac{3x_0^2+2}{2x_0}|+|\dfrac{3x_0^2+3}{2x_0}|$
$\to P=|\dfrac{3x_0^2+2}{2x_0}|+|\dfrac{3x_0^2+3}{2x_0}|$
$\to P=\dfrac{|3x_0^2+2|}{|2x_0|}+\dfrac{|3x_0^2+3|}{|2x_0|}$
$\to P=\dfrac{3x_0^2+2}{|2x_0|}+\dfrac{3x_0^2+3}{|2x_0|}$
$\to P=\dfrac{3x_0^2+2+3x_0^2+3}{|2x_0|}$
$\to P=\dfrac{6x_0^2+5}{|2x_0|}$
Đến đây chỉ cần áp dụng bđt cosi cho $2$ số không âm $6x_0^2, 5$ ta có:
$\to P\ge\dfrac{2\sqrt{6x_0^2\cdot5}}{|2x_0|}$
$\to P\ge\dfrac{2\sqrt{30x_0^2}}{|2x_0|}$
$\to P\ge\dfrac{2\sqrt{30}\cdot |x_0|}{|2x_0|}$
$\to P\ge\dfrac{2\sqrt{30}\cdot |x_0|}{2|x_0|}$
$\to P\ge \sqrt{30}$
