\(DK:x\ge2\)
\(\Leftrightarrow\sqrt{x-1}+\sqrt{3x-5}=x-2\)
\(\Leftrightarrow4x-6+2\sqrt{\left(x-1\right)\left(3x-5\right)}=x^2-4x+4\)
\(\Leftrightarrow2\sqrt{3x^2-8x+5}=x^2-8x+10\)
\(\Leftrightarrow4\left(3x^2-8x+5\right)=x^4+64x^2+100-16x^3-160x+20x^2\)
\(\Leftrightarrow12x^2-32x+20=x^4-16x^3+84x^2-160x+100\)
\(\Leftrightarrow x^4-16x^3+72x^2-128x+80=0\)
\(\Leftrightarrow\left(x^4-10x^3\right)-\left(6x^3-60x^2\right)+\left(12x^2-120x\right)-\left(8x-80\right)=0\)
\(\Leftrightarrow x^3\left(x-10\right)-6x^2\left(x-10\right)+12x\left(x-10\right)-8\left(x-10\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(x^3-6x^2+12x-8\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(x-2\right)^3=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=10\left(n\right)\\x=2\left(n\right)\end{cases}}\)
Vay PT co 2 nghiem \(x=10,x=2\)
