vào đây :
https://coccoc.com/search/math#query=%E2%88%9Ax%2B3%E2%88%924%E2%88%9Ax%E2%88%921%2B%E2%88%9A8%2Bx%2B6%E2%88%9Ax%E2%88%921%3D5+
có lời giải đầy dủ lun
\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{8+x+6\sqrt{x-1}}=5\)
\(\Rightarrow\sqrt{x-1-4\sqrt{x-1}+4}+\sqrt{x-1+6\sqrt{x-1}+9}=5\)
\(\Rightarrow\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}+3\right)^2}=5\)
\(\Rightarrow\left|\sqrt{x-1}-2\right|+\sqrt{x-1}+3=5\left(1\right)\)
+ Khi \(\sqrt{x-1}-2\ge0\Rightarrow\sqrt{x-1}\ge2\Rightarrow x-1\ge4\Rightarrow x\ge5\), (1) trở thành
\(\sqrt{x-1}-2+\sqrt{x-1}+3=5\Rightarrow2\sqrt{x-1}=4\Rightarrow\sqrt{x-1}=2\Rightarrow x=5\)
+ Khi \(\sqrt{x-1}-2< 0\Rightarrow x< 5\) (1) trở thành:
\(2-\sqrt{x-1}+\sqrt{x-1}+3=5\Rightarrow0x=0\)=> có vô số nghiệm
