Bài 5:
1) \(2\sqrt{3x}-4\sqrt{3x}-3\sqrt{3x}=-30\left(x\ge0\right)\)
\(\Leftrightarrow\sqrt{3x}\left(2-4-3\right)=-30\)
\(\Leftrightarrow-5\sqrt{3x}=-30\)
\(\Leftrightarrow\sqrt{3x}=6\)
\(\Leftrightarrow3x=36\)
\(\Leftrightarrow x=12\left(tm\right)\)
2) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}=28\left(x\ge0\right)\)
\(\Leftrightarrow3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}=28\)
\(\Leftrightarrow14\sqrt{2x}=28\)
\(\Leftrightarrow\sqrt{2x}=2\)
\(\Leftrightarrow2x=4\)
\(\Leftrightarrow x=2\left(tm\right)\)
3) \(5\sqrt{12x}-4\sqrt{3x}+2\sqrt{48x}=14\left(x\ge0\right)\)
\(\Leftrightarrow10\sqrt{3x}-4\sqrt{3x}+8\sqrt{3x}=14\)
\(\Leftrightarrow14\sqrt{3x}=14\)
\(\Leftrightarrow\sqrt{3x}=1\)
\(\Leftrightarrow3x=1\)
\(\Leftrightarrow x=\dfrac{1}{3}\left(tm\right)\)
4) \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\sqrt{9x-45}=4\left(x\ge5\right)\)
\(\Leftrightarrow\sqrt{4\left(x-5\right)}+\sqrt{x-5}-\dfrac{1}{3}\cdot3\sqrt{x-5}=4\)
\(\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)
\(\Leftrightarrow2\sqrt{x-5}=4\)
\(\Leftrightarrow\sqrt{x-5}=2\)
\(\Leftrightarrow x-5=4\)
\(\Leftrightarrow x=9\left(tm\right)\)
5: ĐKXĐ: x>=1/2
\(\sqrt{2x-1}=\sqrt{2}-1\)
=>\(2x-1=\left(\sqrt{2}-1\right)^2=3-2\sqrt{2}\)
=>\(2x=3-2\sqrt{2}+1=4-2\sqrt{2}\)
=>\(x=2-\sqrt{2}\)(nhận)
6: ĐKXĐ: x>=-5
\(\sqrt{x+5}=\sqrt{3}-2\)
mà \(\sqrt{3}-2=\sqrt{3}-\sqrt{4}< 0\)
nên phương trình vô nghiệm
7:
ĐKXĐ: x>=-11/3
\(\sqrt{3x+11}=3+\sqrt{2}\)
=>\(3x+11=\left(3+\sqrt{2}\right)^2=11+6\sqrt{2}\)
=>\(3x=6\sqrt{2}\)
=>\(x=2\sqrt{2}\left(nhận\right)\)
8: ĐKXĐ: x>=-38
\(\sqrt{x+38}=3+\sqrt{5}\)
=>\(x+38=\left(3+\sqrt{5}\right)^2=14+6\sqrt{5}\)
=>\(x=14+6\sqrt{5}-38=-24+6\sqrt{5}\)(nhận)
9: ĐKXĐ: x>=-5
\(\sqrt{4x+20}-3\sqrt{x+5}-\dfrac{4}{3}\cdot\sqrt[2]{9x+45}=6\)
=>\(2\sqrt{x+5}-3\sqrt{x+5}-\dfrac{4}{3}\cdot3\sqrt{x+5}=6\)
=>\(-5\sqrt{x+5}=6\)(vô lý)
=>Phương trình vô nghiệm
10: ĐKXĐ: x>=1
\(\sqrt{25x-25}-\dfrac{15}{2}\cdot\sqrt{\dfrac{x-1}{9}}=6+\sqrt{x-1}\)
=>\(5\sqrt{x-1}-\dfrac{15}{2}\cdot\dfrac{\sqrt{x-1}}{3}-\sqrt{x-1}=6\)
=>\(\dfrac{3}{2}\cdot\sqrt{x-1}=6\)
=>\(\sqrt{x-1}=4\)
=>x-1=16
=>x=17(nhận)
11: ĐKXĐ: x>=0
\(\dfrac{3\sqrt{x}-5}{2}-\dfrac{2\sqrt{x}-7}{3}=\sqrt{x}-1\)
=>\(\dfrac{3\left(3\sqrt{x}-5\right)-2\left(2\sqrt{x}-7\right)}{6}=\sqrt{x}-1\)
=>\(9\sqrt{x}-15-4\sqrt{x}+14=6\left(\sqrt{x}-1\right)=6\sqrt{x}-6\)
=>\(5\sqrt{x}-1=6\sqrt{x}-6\)
=>\(-\sqrt{x}=-5\)
=>\(\sqrt{x}=5\)
=>x=25(nhận)
