KT
6 tháng 1 2019 lúc 10:06
\(2x^2-3x+2=x\sqrt{3x-2}\)
\(\Leftrightarrow2x^2-\left(3x-2\right)^2=x\left(3x-2\right)\)
\(\Leftrightarrow2x^2-\left(9x^2-12x+4\right)=3x^2-2x\)
\(\Leftrightarrow-7x^2+12x-4=3x^2-2x\)
\(\Leftrightarrow10x^2-14x=-4\)
\(\Leftrightarrow x^2-\dfrac{7}{5}x=-\dfrac{2}{5}\)
\(\Leftrightarrow\left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{7}{10}=\dfrac{3}{10}\\x-\dfrac{7}{10}=-\dfrac{3}{10}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{2}{5}\end{matrix}\right.\)
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