Giải pt: căn(4x-1) + căn(3x-2)=(x+1)/5

Đáp án:

$ x=174\pm 10\sqrt{295}$

Giải thích các bước giải:

ĐKXĐ: $x\ge \dfrac{2}{3}$

Ta có:

$\sqrt{4x-1}+\sqrt{3x-2}=\dfrac{x+1}{5}$

$\rightarrow\sqrt{4x-1}+\sqrt{3x-2}=\dfrac{4x-1-(3x-2)}{5}$

$\rightarrow\sqrt{4x-1}+\sqrt{3x-2}=\dfrac{(\sqrt{4x-1}-\sqrt{3x-2})(\sqrt{4x-1}+\sqrt{3x-2})}{5}$

$\rightarrow 1=\dfrac{\sqrt{4x-1}-\sqrt{3x-2}}{5}$

$\rightarrow \sqrt{4x-1}-\sqrt{3x-2}=5$

$\rightarrow \sqrt{4x-1}=\sqrt{3x-2}+5$

$\rightarrow (\sqrt{4x-1})^2=(\sqrt{3x-2}+5)^2$

$\rightarrow 4x-1=3x-2+10\sqrt{3x-2}+25$

$\rightarrow x-24=10\sqrt{3x-2}$

$\rightarrow (x-24)^2=(10\sqrt{3x-2})^2$

$\rightarrow x^2-48x+24^2=100(3x-2)$

$\rightarrow x^2-348x+776=0$

$\rightarrow x=\dfrac{348\pm 20\sqrt{295}}{2}$

$\rightarrow x=174\pm 10\sqrt{295}$