19: ĐKXĐ: x>=-1
\(3\sqrt{4x+4}-\sqrt{9x+9}-8\sqrt{\dfrac{x+1}{16}}=5\)
=>\(3\cdot2\sqrt{x+1}-3\sqrt{x+1}-8\cdot\dfrac{\sqrt{x+1}}{4}=5\)
=>\(\sqrt{x+1}=5\)
=>x+1=25
=>x=24(nhận)
20: ĐKXĐ: x>=5
\(\sqrt{9x-45}-\sqrt{x-5}=4-\dfrac{1}{2}\cdot\sqrt{4x-20}\)
=>\(3\sqrt{x-5}-\sqrt{x-5}+\dfrac{1}{2}\cdot2\sqrt{x-5}=4\)
=>\(3\sqrt{x-5}=4\)
=>\(\sqrt{x-5}=\dfrac{4}{3}\)
=>\(x-5=\left(\dfrac{4}{3}\right)^2=\dfrac{16}{9}\)
=>\(x=5+\dfrac{16}{9}=\dfrac{61}{9}\left(nhận\right)\)
21: ĐKXĐ: x>=2
\(\sqrt{4x-8}-\dfrac{1}{3}\cdot\sqrt{9x-18}=3\sqrt{x-2}-1\)
=>\(2\sqrt{x-2}-\dfrac{1}{3}\cdot3\sqrt{x-2}-3\sqrt{x-2}=-1\)
=>\(-2\sqrt{x-2}=-1\)
=>\(\sqrt{x-2}=\dfrac{1}{2}\)
=>\(x-2=\dfrac{1}{4}\)
=>\(x=2+\dfrac{1}{4}=\dfrac{9}{4}\left(nhận\right)\)
22: ĐKXĐ: x>=-2
\(\sqrt{9x+18}+\dfrac{1}{4}\cdot\sqrt{16x+32}-2\sqrt{x+2}=4\)
=>\(3\sqrt{x+2}+\dfrac{1}{4}\cdot4\sqrt{x+2}-2\sqrt{x+2}=4\)
=>\(2\sqrt{x+2}=4\)
=>\(\sqrt{x+2}=2\)
=>\(x+2=2^2=4\)
=>x=2(nhận)
23: ĐKXĐ: x>=3
\(\sqrt{4x-12}+\dfrac{1}{3}\cdot\sqrt{9x-27}=4+\sqrt{x-3}\)
=>\(2\sqrt{x-3}+\dfrac{1}{3}\cdot3\sqrt{x-3}-\sqrt{x-3}=4\)
=>\(2\sqrt{x-3}=4\)
=>x-3=4
=>x=7(nhận)
24: ĐKXĐ: x>=2
\(\sqrt{4x-8}-5\sqrt{x-2}+\dfrac{2}{3}\cdot\sqrt{9x-18}+1=0\)
=>\(2\sqrt{x-2}-5\sqrt{x-2}+\dfrac{2}{3}\cdot3\sqrt{x-2}+1=0\)
=>\(1-\sqrt{x-2}=0\)
=>x-2=1
=>x=3(nhận)
25: ĐKXĐ: x>=4
\(5\sqrt{4x-16}-\dfrac{7}{3}\cdot\sqrt{9x-36}=36-3\sqrt{x-4}\)
=>\(5\cdot2\sqrt{x-4}-\dfrac{7}{3}\cdot3\sqrt{x-4}+3\sqrt{x-4}=36\)
=>\(6\sqrt{x-4}=36\)
=>\(\sqrt{x-4}=6\)
=>\(x-4=6^2=36\)
=>x=36+4=40(nhận)
26: ĐKXĐ: x>=3
\(\sqrt[]{x-3}+\sqrt{9x-27}-\dfrac{1}{2}\cdot\sqrt{4x-12}=6\)
=>\(\sqrt{x-3}+3\sqrt{x-3}-\dfrac{1}{2}\cdot2\sqrt{x-3}=6\)
=>\(3\sqrt{x-3}=6\)
=>\(\sqrt{x-3}=2\)
=>\(x-3=2^2=4\)
=>x=4+3=7(nhận)
27: ĐKXĐ: x>=5
\(\sqrt{4x-20}+\sqrt{x-5}=4+3\sqrt{\dfrac{x-5}{9}}\)
=>\(2\sqrt{x-5}+\sqrt{x-5}-3\cdot\dfrac{\sqrt{x-5}}{3}=4\)
=>\(2\sqrt{x-5}=4\)
=>\(\sqrt{x-5}=2\)
=>\(x-5=2^2=4\)
=>x=4+5=9(nhận)
29: ĐKXĐ: x>=3
\(\sqrt{4x-12}-\sqrt{9x-27}+\sqrt{\dfrac{25x-75}{4}}-3=0\)
=>\(2\sqrt{x-3}-3\sqrt{x-3}+\dfrac{5}{2}\cdot\sqrt{x-3}=3\)
=>\(\dfrac{3}{2}\sqrt{x-3}=3\)
=>\(\sqrt{x-3}=2\)
=>\(x-3=2^2=4\)
=>x=4+3=7(nhận)
31: ĐKXĐ: x>=1
\(\sqrt{9x-9}-3\sqrt{x-1}+\dfrac{5}{2}\sqrt{16x-16}=30\)
=>\(3\sqrt{x-1}-3\sqrt{x-1}+\dfrac{5}{2}\cdot4\sqrt{x-1}=30\)
=>\(10\sqrt{x-1}=30\)
=>\(\sqrt{x-1}=3\)
=>\(x-1=3^2=9\)
=>x=9+1=10(nhận)
33: ĐKXĐ: x>=1
\(\sqrt{x-1}-\dfrac{1}{2}\cdot\sqrt{4x-4}+\sqrt{\dfrac{18x-18}{2}}=6\)
=>\(\sqrt{x-1}-\dfrac{1}{2}\cdot2\sqrt{x-1}+\sqrt{9x-9}=6\)
=>\(\sqrt{x-1}-\sqrt{x-1}+3\sqrt{x-1}=6\)
=>\(3\sqrt{x-1}=6\)
=>\(\sqrt{x-1}=2\)
=>\(x-1=2^2=4\)
=>x=4+1=5(nhận)
