52.
a) \(\sqrt{2x-1}=\sqrt{2}-1\) (ĐK: \(x\ge\dfrac{1}{2}\))
\(\Leftrightarrow2x-1=\left(\sqrt{2}-1\right)^2\)
\(\Leftrightarrow2x-1=2-2\sqrt{2}+1\)
\(\Leftrightarrow2x=3-2\sqrt{2}+1\)
\(\Leftrightarrow2x=4-2\sqrt{2}\)
\(\Leftrightarrow x=\dfrac{4-2\sqrt[]{2}}{2}\)
\(\Leftrightarrow x=2-\sqrt{2}\left(tm\right)\)
b) \(\sqrt{3x+11}=3+\sqrt{2}\) (ĐK: \(x\ge-\dfrac{11}{3}\))
\(\Leftrightarrow3x+11=\left(3+\sqrt{2}\right)^2\)
\(\Leftrightarrow3x+11=9+6\sqrt{2}+2\)
\(\Leftrightarrow3x+11=11+6\sqrt{2}\)
\(\Leftrightarrow3x=11-11+6\sqrt{2}\)
\(\Leftrightarrow3x=6\sqrt{2}\)
\(\Leftrightarrow x=\dfrac{6\sqrt{2}}{3}\)
\(\Leftrightarrow x=2\sqrt{2}\left(tm\right)\)
c) \(\sqrt{x+5}=\sqrt{3}-2\) (ĐK: \(x\ge-5\))
\(\Leftrightarrow x+5=\left(\sqrt{3}-2\right)^2\)
\(\Leftrightarrow x+5=3-4\sqrt{3}+4\)
\(\Leftrightarrow x+5=7-4\sqrt{3}\)
\(\Leftrightarrow x=7-4\sqrt{3}-5\)
\(\Leftrightarrow x=2-4\sqrt{3}\left(tm\right)\)
d) \(\sqrt{x+38}=3+\sqrt{5}\) (ĐK: \(x\ge-38\))
\(\Leftrightarrow x+38=\left(3+\sqrt{5}\right)^2\)
\(\Leftrightarrow x+38=9+6\sqrt{5}+5\)
\(\Leftrightarrow x+38=14+6\sqrt{5}\)
\(\Leftrightarrow x=14-38+6\sqrt{5}\)
\(\Leftrightarrow x=6\sqrt{5}-24\left(tm\right)\)
