Toán Lớp 8: Hộ em gấp với ạ
Bài 2: Cho biểu thức: A = (2√x-9)/(x-5√x+6)-(√x+3)/(√x-2)-(2√x+1)/(3 – √x)
a) Rút gọn A
b) Tìm x để A = -3
c) Tìm x để A < 1
d) Tìm x nguyên để A nguyên
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Toán Lớp 8: Hộ em gấp với ạ
Bài 2: Cho biểu thức: A = (2√x-9)/(x-5√x+6)-(√x+3)/(√x-2)-(2√x+1)/(3 – √x)
a) Rút gọn A
b) Tìm x để A = -3
c) Tìm x để A < 1
d) Tìm x nguyên để A nguyên
Comments ( 1 )
B2:\\
a)\dfrac{{\sqrt x + 1}}{{\sqrt x – 3}}\\
b)x = 4\\
c)x < 9\\
d)\left[ \begin{array}{l}
x = 49\\
x = 25\\
x = 16\\
x = 1
\end{array} \right.
\end{array}\)
B2:\\
a)DK:x \ge 0;x \ne \left\{ {4;9} \right\}\\
A = \dfrac{{2\sqrt x – 9}}{{x – 5\sqrt x + 6}} – \dfrac{{\sqrt x + 3}}{{\sqrt x – 2}} – \dfrac{{2\sqrt x + 1}}{{3 – \sqrt x }}\\
= \dfrac{{2\sqrt x – 9 – \left( {\sqrt x + 3} \right)\left( {\sqrt x – 3} \right) + \left( {2\sqrt x + 1} \right)\left( {\sqrt x – 2} \right)}}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{2\sqrt x – 9 – x + 9 + 2x – 3\sqrt x – 2}}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{x – \sqrt x – 2}}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{\left( {\sqrt x – 2} \right)\left( {\sqrt x + 1} \right)}}{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 3} \right)}}\\
= \dfrac{{\sqrt x + 1}}{{\sqrt x – 3}}\\
b)A = – 3\\
\to \dfrac{{\sqrt x + 1}}{{\sqrt x – 3}} = – 3\\
\to \sqrt x + 1 = – 3\sqrt x + 9\\
\to 4\sqrt x = 8\\
\to \sqrt x = 2\\
\to x = 4\\
c)A < 1\\
\to \dfrac{{\sqrt x + 1}}{{\sqrt x – 3}} < 1\\
\to \dfrac{{\sqrt x + 1 – \sqrt x + 3}}{{\sqrt x – 3}} < 0\\
\to \dfrac{4}{{\sqrt x – 3}} < 0\\
\to \sqrt x – 3 < 0\\
\to x < 9\\
d)A = \dfrac{{\sqrt x – 3 + 4}}{{\sqrt x – 3}}\\
= 1 + \dfrac{4}{{\sqrt x – 3}}\\
A \in Z \to \dfrac{4}{{\sqrt x – 3}} \in Z\\
\to \sqrt x – 3 \in U\left( 4 \right)\\
\to \left[ \begin{array}{l}
\sqrt x – 3 = 4\\
\sqrt x – 3 = 2\\
\sqrt x – 3 = 1\\
\sqrt x – 3 = – 1\\
\sqrt x – 3 = – 2\\
\sqrt x – 3 = – 4\left( l \right)
\end{array} \right. \to \left[ \begin{array}{l}
x = 49\\
x = 25\\
x = 16\\
x = 4\left( l \right)\\
x = 1
\end{array} \right.
\end{array}\)