\(\sqrt{x+3+2\sqrt{3x}}-\sqrt{x+3-2\sqrt{3x}}=2\sqrt{2}\)
Bình phương 2 vế, ta được:
\(x+3+2\sqrt{3}-2\sqrt{\left(x+3+2\sqrt{3x}\right)\left(x+3-2\sqrt{3}\right)}+x+3-2\sqrt{3}=8\)
\(\Leftrightarrow2x+6-2\sqrt{\left(x+3\right)^2-12x}=8\)
\(\Leftrightarrow2\left(x+3-\sqrt{\left(x+3\right)^2-12x}\right)=8\)
\(\Leftrightarrow x+3-\sqrt{\left(x+3\right)-12x}=4\)
\(\Leftrightarrow x-1=\sqrt{\left(x+3\right)^2-12x}\)
Bình phương 2 vế, ta được:
\(\left(x-1\right)^2=\left(x+3\right)^2-12x\)
\(\Leftrightarrow x^2-2x+1=x^2+6x+9-12x\)
\(\Leftrightarrow4x=8\Leftrightarrow x=2\)
\(\sqrt{3x+6\sqrt{3x}+9}-\sqrt{3x-6\sqrt{3x}+9}=2\sqrt{6}..\)
\(\sqrt{3x}+3-\left|\sqrt{3x}-3\right|=2\sqrt{6}..\)
