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Giải các phương trình sau:
a) \(5{x^2} – 7x = 0\)
b) \(6{x^2} + 3\sqrt 2 x = 0\)
c) \( – 8{x^2} + 3x = 0\)
d) \({x^2} – 12 = 0\)
e) \(5{x^2} – 15 = 0\)
f) \(\dfrac{2}{3}{x^2} – \dfrac{4}{{15}} = 0\)
Đưa phương trình đã cho về dạng phương trình tích \(a.b = 0 \Leftrightarrow \left[ \begin{array}{l}a = 0\\b = 0\end{array} \right.\)
a) \(5{x^2} – 7x = 0 \)
\(\Leftrightarrow x\left( {5x – 7} \right) = 0 \)
\(\Leftrightarrow \left[ \begin{array}{l}x = 0\\5x – 7 = 0\end{array} \right.\)
\(\Leftrightarrow \left[ \begin{array}{l}x = 0\\x = \dfrac{7}{5}\end{array} \right.\)
b) \(6{x^2} + 3\sqrt 2 x = 0\)
\(\Leftrightarrow 3x\left( {2x + \sqrt 2 } \right) = 0\)
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\(\Leftrightarrow \left[ \begin{array}{l}3x = 0\\2x + \sqrt 2 = 0\end{array} \right.\)
\(\Leftrightarrow \left[ \begin{array}{l}x = 0\\x = – \dfrac{{\sqrt 2 }}{2}\end{array} \right.\)
c) \( – 8{x^2} + 3x = 0\)
\(\Leftrightarrow x\left( { – 8x + 3} \right) = 0 \)
\(\Leftrightarrow \left[ \begin{array}{l}x = 0\\ – 8x + 3 = 0\end{array} \right. \)
\(\Leftrightarrow \left[ \begin{array}{l}x = 0\\x = \dfrac{3}{8}\end{array} \right.\)
d) \({x^2} – 12 = 0\)
\(\Leftrightarrow {x^2} = 12 \)
\(\Leftrightarrow x = \pm 2\sqrt 3 \)
e) \(5{x^2} – 15 = 0 \)
\(\Leftrightarrow 5{x^2} = 15\)
\(\Leftrightarrow {x^2} = 3\)
\(\Leftrightarrow x = \pm \sqrt 3 \)
f) \(\dfrac{2}{3}{x^2} – \dfrac{4}{{15}} = 0\)
\(\Leftrightarrow \dfrac{2}{3}{x^2} = \dfrac{4}{{15}}\)
\(\Leftrightarrow {x^2} = \dfrac{2}{5} \)
\(\Leftrightarrow x = \pm \dfrac{{\sqrt {10} }}{5}\)