Giải phương trình ( tìm đkxđ) a) $\sqrt{2x-3}$=$\sqrt{5}$ b) $\sqrt{3x-2}$=$\sqrt{12x-8}$ + $\sqrt{27x-18}$=6 c) $\sqrt{50x}$-75+$\sqrt{18x-27}$+5$\sqrt{2x-3}$=26

Đáp án:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ x=5\\ b.\ x=\frac{11}{3}\\ c.\ x=\frac{7}{2} \end{array}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ \sqrt{2x-5} =\sqrt{5} ;\ ĐKXĐ:x\geqslant \frac{5}{2}\\ \Leftrightarrow 2x-5=5\\ \Leftrightarrow 2x=10\\ \Leftrightarrow x=5\\ b.\ \sqrt{3x-2} -\sqrt{12x-8} +\sqrt{27x-18} =6\\ \Leftrightarrow \sqrt{3x-2} -\sqrt{2^{2}( 3x-2)} +\sqrt{3^{2}( 3x-2)} =6\\ \Leftrightarrow \sqrt{3x-2} -2\sqrt{3x-2} +3\sqrt{3x-2} =6\\ \Leftrightarrow 2\sqrt{3x-2} =6\\ \Leftrightarrow \sqrt{3x-2} =3\\ \Leftrightarrow 3x-2=9\\ \Leftrightarrow 3x=11\\ \Leftrightarrow x=\frac{11}{3}\\ c.\ \sqrt{50x-75} +\sqrt{18x-27} +5\sqrt{2x-3} =26\\ \Leftrightarrow \sqrt{5^{2}( 2x-3)} +\sqrt{3^{2}( 2x-3)} +5\sqrt{2x-3} =26\\ \Leftrightarrow 5\sqrt{2x-3} +3\sqrt{2x-3} +5\sqrt{2x-3} =26\\ \Leftrightarrow 13\sqrt{2x-3} =26\\ \Leftrightarrow \sqrt{2x-3} =2\\ \Leftrightarrow 2x-3=4\\ \Leftrightarrow 2x=7\\ \Leftrightarrow x=\frac{7}{2} \end{array}$

#andy

\[\begin{array}{l}
a)\sqrt {2x - 5}  = \sqrt 5 \,\,\,\,DKXD:x \ge \frac{5}{2}\\
 \Leftrightarrow 2x - 5 = 5\\
 \Leftrightarrow 2x = 10\\
 \Leftrightarrow x = 5\\
b)\sqrt {3x - 2}  - \sqrt {12x - 8}  + \sqrt {27x - 16}  = 6\\
 \Leftrightarrow \sqrt {3x - 2}  - \sqrt {4\left( {3x - 2} \right)}  + \sqrt {9\left( {3x - 2} \right)}  = 6\\
 \Leftrightarrow \sqrt {3x - 2}  - 2\sqrt {3x - 2}  + 3\sqrt {3x - 2}  = 6\\
 \Leftrightarrow 2\sqrt {3x - 2}  = 6\\
 \Leftrightarrow \sqrt {3x - 2}  = 3\\
 \Leftrightarrow 3x - 2 = 3\\
 \Leftrightarrow x = \frac{{11}}{3}\\
c.\;\sqrt {50x - 75}  + \sqrt {18x - 27}  + 5\sqrt {2x - 3}  = 26\\
 \Leftrightarrow \sqrt {25(2x - 3)}  + \sqrt {9(2x - 3)}  + 5\sqrt {2x - 3}  = 26\\
 \Leftrightarrow 5\sqrt {2x - 3}  + 3\sqrt {2x - 3}  + 5\sqrt {2x - 3}  = 26\\
 \Leftrightarrow 13\sqrt {2x - 3}  = 26\\
 \Leftrightarrow \sqrt {2x - 2}  = 2\\
 \Leftrightarrow 2x - 2 = 4\\
 \Leftrightarrow x = \frac{7}{2}
\end{array}\]