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:

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