Question

1, cho A= căn 3x-5/x-1
a, tìm đk của x để A có nghĩa
b,Tìm x để A=3
#giúp mk vs ạ

Answer 1

a, ĐKXĐ : \(\left\{{}\begin{matrix}\dfrac{3x-5}{x-1}\ge0\\x-1\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-5\ge0\\x-1>0\end{matrix}\right.\\\left\{{}\begin{matrix}3x-5\le0\\x-1< 0\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\dfrac{5}{3}\\x>1\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\dfrac{5}{3}\\x< 1\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\ge\dfrac{5}{3}\\x< 1\end{matrix}\right.\)

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b, Ta có : \(A=\sqrt{\dfrac{3x-5}{x-1}}=3\)

\(\Leftrightarrow3x-5=9x-9\)

\(\Leftrightarrow x=\dfrac{2}{3}\left(TM\right)\)

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