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