Toán Lớp 9: Cho B= 2 căn x-5/ căn x+2
1. Tìm B tại x = 16
2. Tìm x biết A=3/4
3.Tìm x biết A< 1/3
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Toán Lớp 9: Cho B= 2 căn x-5/ căn x+2
1. Tìm B tại x = 16
2. Tìm x biết A=3/4
3.Tìm x biết A< 1/3
Comments ( 1 )
1)B = \dfrac{1}{2}\\
2)x = \dfrac{{676}}{{25}}\\
3)0 \le x < \dfrac{{289}}{{25}}
\end{array}\)
1)DK:x \ge 0\\
Thay:x = 16\\
\to B = \dfrac{{2\sqrt {16} – 5}}{{\sqrt {16} + 2}} = \dfrac{{2.4 – 5}}{{4 + 2}}\\
= \dfrac{3}{6} = \dfrac{1}{2}\\
2)B = \dfrac{3}{4}\\
\to \dfrac{{2\sqrt x – 5}}{{\sqrt x + 2}} = \dfrac{3}{4}\\
\to 8\sqrt x – 20 = 3\sqrt x + 6\\
\to 5\sqrt x = 26\\
\to \sqrt x = \dfrac{{26}}{5}\\
\to x = \dfrac{{676}}{{25}}\\
3)B < \dfrac{1}{3}\\
\to \dfrac{{2\sqrt x – 5}}{{\sqrt x + 2}} < \dfrac{1}{3}\\
\to \dfrac{{6\sqrt x – 15 – \sqrt x – 2}}{{3\left( {\sqrt x + 2} \right)}} < 0\\
\to 5\sqrt x – 17 < 0\left( {do:\sqrt x + 2 > 0\forall x \ge 0} \right)\\
\to \sqrt x < \dfrac{{17}}{5}\\
\to 0 \le x < \dfrac{{289}}{{25}}
\end{array}\)