Toán Lớp 9: Bài 1 Giải phương trình : căn bậc 3 x-2+ căn x-1=3
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Toán Lớp 9: Bài 1 Giải phương trình : căn bậc 3 x-2+ căn x-1=3
Comments ( 1 )
x = 17\\
x = 2
\end{array} \right.\)
DK:x \ge 1\\
\sqrt {3x – 2} + \sqrt {x – 1} = 3\\
\to 3x – 2 + 2\sqrt {\left( {3x – 2} \right)\left( {x – 1} \right)} + x – 1 = 9\\
\to 4x – 3 + 2\sqrt {3{x^2} – 5x + 2} = 9\\
\to 2\sqrt {3{x^2} – 5x + 2} = 12 – 4x\\
\to \sqrt {3{x^2} – 5x + 2} = 6 – 2x\\
\to 3{x^2} – 5x + 2 = 36 – 24x + 4{x^2}\\
\to {x^2} – 19x + 34 = 0\\
\to \left( {x – 2} \right)\left( {x – 17} \right) = 0\\
\to \left[ \begin{array}{l}
x = 17\\
x = 2
\end{array} \right.
\end{array}\)