√3x + 4 - √2x-1 = √x+3

Đáp án:

$ x=\dfrac{-5+\sqrt[]{57}}{4}$ 

Giải thích các bước giải:

Đkxđ: $x\ge \dfrac{1}{2}$

$\sqrt[]{3x+4}-\sqrt[]{2x-1}=\sqrt[]{x+3}$ 

$\rightarrow\sqrt[]{3x+4}=\sqrt[]{2x-1}+\sqrt[]{x+3}$

$\rightarrow(\sqrt[]{3x+4})^2=(\sqrt[]{2x-1}+\sqrt[]{x+3})^2$

$\rightarrow 3x+4=3x+2+2\sqrt[]{2x-1}\sqrt[]{x+3}$

$\rightarrow \sqrt[]{2x^2+5x-3}=1$

$\rightarrow 2x^2+5x-3=1$

$\rightarrow 2x^2+5x-4=0$

$\rightarrow x=\dfrac{-5\pm\sqrt[]{57}}{4}\rightarrow x=\dfrac{-5+\sqrt[]{57}}{4}(x\ge \dfrac{1}{2})$