ĐKXĐ: \(x\ge\frac{7}{2}\)
\(\sqrt{x+5}=2\sqrt{x}-2\sqrt{2x-7}\)
\(\Leftrightarrow x+5=2^2\left(\sqrt{x}-\sqrt{2x-7}\right)^2\)
\(\Leftrightarrow x+5=4\left(x+2x-7-2\sqrt{x\left(2x-7\right)}\right)\)
\(\Leftrightarrow x+5=4\left(3x-7-2\sqrt{2x^2-7x}\right)\)
\(\Leftrightarrow x+5=12x-28-8\sqrt{2x^2-7x}\)
\(\Leftrightarrow8\sqrt{2x^2-7x}=11x-33\)
\(\Leftrightarrow2x^2-7x=\left(\frac{11x-33}{8}\right)^2\)
\(\Leftrightarrow2x^2-7x=\frac{121x^2-726x+1089}{64}\)
\(\Leftrightarrow128x^2-448x=121x^2-726x+1089\)
\(\Leftrightarrow7x^2+278x-1089=0\)
\(\Leftrightarrow x=\overset{+}{-}\frac{8\sqrt{421}}{7}-19\frac{6}{7}\) ( ko t/m)
Vậy pt vô nghiệm
