1 reply to this topic

[rainbow99]

Giải phương trình: 

1) $(3x+1)\sqrt{x^{2}+3}=3x^{2}+2x+3$

2) $\frac{x^{2}}{1-\sqrt{x}}=x-2\sqrt{x}+2$ (Nghiệm là $x=4+2\sqrt{3}$)

Edited by rainbow99, 16-02-2015 - 20:38.

[baotranthaithuy]

1.

đặt $y=\sqrt{x^2+3} (y\geq 0)$

 

$\Rightarrow  (3x+1)y=y^2+2x^2+2x$

 

$\Leftrightarrow y^2-(3x+1)y+2x^2+2x=0$

 

$\Delta =(3x+1)^2-4(2x^2+2x)=x^2-2x+1=(x+1)^2$

 

$\Rightarrow  \begin{bmatrix}y=\dfrac{3x+1-x-1}{2}=x & \\ y=\dfrac{3x+1+x+1}{2}=2x+1 & \end{bmatrix}$