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Giải thích các bước giải:
$\text{CM$:5x^2+15x-17=0$}$ vô nghiệm
$5x^2+15x-17=0$
$⇒5(x^2+3x-\dfrac{17}{5})=0$
$⇒x^2+3x-\dfrac{17}{5}=0$
$⇒x^2+2.x.\dfrac{3}{2}+(\dfrac{3}{2})^2-(\dfrac{3}{2})^2-\dfrac{17}{5}=0$
$⇒x^2+2.x.\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{9}{4}-\dfrac{17}{5}=0$
$⇒(x+\dfrac{3}{2})^2-\dfrac{113}{20}=0$
$⇒(x+\dfrac{3}{2})^2=\dfrac{113}{20}$
$⇒x+\dfrac{3}{2}=±\sqrt{\dfrac{113}{20}}$
$⇒x+\dfrac{3}{2}=±\dfrac{\sqrt{565}}{10}$
$⇒\left[ \begin{array}{l}x+\dfrac{3}{2}=\dfrac{\sqrt{565}}{10}\\x+\dfrac{3}{2}=-\dfrac{\sqrt{565}}{10}\end{array} \right.⇒\left[ \begin{array}{l}x=\dfrac{\sqrt{565}-15}{10}\\x=-\dfrac{\sqrt{565}+15}{10}\end{array} \right.$
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