Toán Lớp 10: Tích các nghiệm của pt 2x+1/3x+2=x+1/x-2 là
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Toán Lớp 10: Tích các nghiệm của pt 2x+1/3x+2=x+1/x-2 là
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DK:x \ne \left\{ { – \dfrac{2}{3};2} \right\}\\
\dfrac{{2x + 1}}{{3x + 2}} = \dfrac{{x + 1}}{{x – 2}}\\
\to \left( {2x + 1} \right)\left( {x – 2} \right) = \left( {3x + 2} \right)\left( {x + 1} \right)\\
\to 2{x^2} – 3x – 2 = 3{x^2} + 5x + 2\\
\to {x^2} + 8x + 4 = 0\\
\to \left[ \begin{array}{l}
x = – 4 + 2\sqrt 3 \\
x = – 4 – 2\sqrt 3
\end{array} \right.\\
\left( { – 4 + 2\sqrt 3 } \right)\left( { – 4 – 2\sqrt 3 } \right)\\
= – \left( { – 4 + 2\sqrt 3 } \right)\left( {4 + 2\sqrt 3 } \right)\\
= – \left( {12 – 16} \right) = 4
\end{array}\)