[ Toán 8 ] Phân thức

T

transformers123

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

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

$\iff P=\dfrac{x^2+x+1}{x^2+2x+1}$

$\iff \dfrac{4P}{3}=\dfrac{4x^2+4x+4}{3x^2+6x+3}$

$\iff \dfrac{4P}{3}=\dfrac{3x^2+6x+3+x^2-2x+1}{3x^2+6x+3}$

$\iff \dfrac{4P}{3}=\dfrac{(x-1)^2}{3x^2+6x+3}+1$

$\Longrightarrow \dfrac{4P}{3} \ge 1$

$\iff P \ge \dfrac{3}{4}$

Dấu "=" xảy ra khi $x-1=0 \iff x=1$

Bên dưới có nút "đúng", có gì bạn bấm vào =))
 
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