a) \(\sqrt{2x+4+6\sqrt{2x-5}}-\sqrt{2x-4-2\sqrt{2x-5}}\)
\(=\sqrt{2x-5+2\cdot\sqrt{2x-5}\cdot3+9}-\sqrt{2x-5-2\cdot\sqrt{2x-5}\cdot3+9}\)
\(=\sqrt{\left(\sqrt{2x-5}+3\right)^2}-\sqrt{\left(\sqrt{2x-5}-3\right)^2}\)
\(=\sqrt{2x-5}+3-\left|\sqrt{2x-5}-3\right|\)
b) \(\sqrt{a+6+6\sqrt{a-3}}+\sqrt{a+6-6\sqrt{a-3}}\)
\(=\sqrt{a-3+2\cdot\sqrt{a-3}\cdot3+9}+\sqrt{a-3-2\cdot\sqrt{a-3}\cdot3+9}\)
\(=\sqrt{\left(\sqrt{a-3}+3\right)^2}+\sqrt{\left(\sqrt{a-3}-3\right)^2}\)
\(=\sqrt{a-3}+3+\left|\sqrt{a-3}-3\right|\)
a) + ĐK : \(x\ge\frac{5}{2}\)
\(A=\sqrt{2x-5+6\sqrt{2x-5}+9}-\sqrt{2x-5-2\sqrt{2x-5}+1}\)
\(=\sqrt{\left(\sqrt{2x-5}+3\right)^2}-\sqrt{\left(\sqrt{2x-5}-1\right)^2}\)
\(=\sqrt{2x-5}+3-\left|\sqrt{2x-5}-1\right|\)
+ TH1: \(x\ge3\) ta có :
\(A=\sqrt{2x-5}+3-\sqrt{2x-5}+1=4\)
+ TH2 : \(\frac{5}{2}\le x< 3\) ta có :
\(A=\sqrt{2x-5}+3+\sqrt{2x-5}-1\)
\(=2\sqrt{2x-5}+2\)
