Giải thích các bước giải:
a.$2008x^2-4x+3=2007x\sqrt{4x-3}$
$\to 2008x^2-2007x\sqrt{4x-3}-(4x-3)=0$
$\to (2008x+\sqrt{4x-3})(x-\sqrt{4x-3})=0$
$\to x-\sqrt{4x-3}=0,x\ge \dfrac 34$
$\to x=\sqrt{4x-3}$
$\to x^2=4x-3$
$\to (x-1)(x-3)=0\to x\in\{1,3\}$
b.$x^2+2=(2x-1)\sqrt{x+2}\to x>\dfrac 12$
$\to (x^2+2)^2=(2x-1)^2(x+2)$
$\to x^4+4x+4=4x^3+4x^2-7x+2$
$\to x^4-4x^3+7x+2=0$
$\to (x+1)(x-2)(x^2-3x-1)=0$
$\to x\in\{2,\dfrac{2+\sqrt{13}}{2}\}$
c.$3(x^2-x+1)=8\sqrt{x^3+x}$
$\to 3(x^2+1)-8\sqrt{x(x^2+1)}-3x=0$
$\to (3\sqrt{x^2+1}+\sqrt{x})(\sqrt{x^2+1}-3\sqrt{x})=0$
$\to \sqrt{x^2+1}-3\sqrt{x}=0$
$\to \sqrt{x^2+1}=3\sqrt{x}$
$\to x=\dfrac{9\pm\sqrt{77}}{2}$