[tex]5x^{3}-22x^{2}+22x-6+\sqrt{4x-3}=0[/tex]
ĐKXĐ: [tex]x\geq \frac{3}{4}[/tex]
[tex]5x^{3}-22x^{2}+22x-6+\sqrt{4x-3}=0\\\Leftrightarrow (5x^{3}-22x^{2}+23x-6)+(\sqrt{4x-3}-x)=0\\\Leftrightarrow (x-1)(x-3)(5x-2)+\frac{4x-3-x^2}{\sqrt{4x-3}+x}=0\\\Leftrightarrow (x-1)(x-3)(5x-2)-\frac{(x-1)(x-3)}{\sqrt{4x-3}+x}=0\\\Leftrightarrow (x-1)(x-3)\left ( 5x-2-\frac{1}{\sqrt{4x-3}+x} \right )=0[/tex]
Th1: [TEX](x-1)(x-3)=0\Leftrightarrow...[/TEX]
Th2: [tex]5x-2-\frac{1}{\sqrt{4x-3}+x} =0\\\Leftrightarrow 5x-2=\frac{1}{\sqrt{4x-3}+x}(*)[/tex]
Vì [tex]x\geq \frac{3}{4}\Rightarrow \left\{\begin{matrix} 5x-2\geq \dfrac{7}{4}\\\dfrac{1}{\sqrt{4x-3}+x}\leq \dfrac{4}{3} \end{matrix}\right.[/tex]
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