Giải các phương trình sau: a) √5x+3=3x-7 b) 7√x²-2x+2=2x²-4x+9 c) √3x²-2x-1=3x+1 d) √4x²-x+1=2x-3 e) x-√2x-5=4

Đáp án:

$\begin{array}{l}
a)\sqrt {5x + 3}  = 3x - 7\left( {dkxd:x \ge \frac{7}{3}} \right)\\
 \Rightarrow 5x + 3 = {\left( {3x - 7} \right)^2}\\
 \Rightarrow 5x + 3 = 9{x^2} - 42x + 49\\
 \Rightarrow 9{x^2} - 42x + 46 = 0\\
 \Rightarrow x = \frac{{7 + \sqrt 3 }}{3}\\
c)\sqrt {3{x^2} - 2x - 1}  = 3x + 1\left( {dkxd:x \ge  - \frac{1}{3}} \right)\\
 \Rightarrow 3{x^2} - 2x - 1 = 9{x^2} + 6x + 1\\
 \Rightarrow 6{x^2} + 8x + 2 = 0\\
 \Rightarrow x =  - \frac{1}{3}\\
e)x - \sqrt {2x - 5}  = 4\\
 \Rightarrow \sqrt {2x - 5}  = x - 4\left( {dkxd:x \ge 4} \right)\\
 \Rightarrow 2x - 5 = {x^2} - 8x + 16\\
 \Rightarrow {x^2} - 10x + 21 = 0\\
 \Rightarrow x = 7
\end{array}$