\(x+\sqrt{5+\sqrt{x-1}}=6\)
Đk:\(x\ge1\)
\(pt\Leftrightarrow\sqrt{5+\sqrt{x-1}}=6-x\)
\(\Leftrightarrow5+\sqrt{x-1}=x^2-12x+36\)
\(\Leftrightarrow\sqrt{x-1}=x^2-12x+31\)
\(\Leftrightarrow x-1=x^4-24x^3+206x^2-744x+961\)
\(\Leftrightarrow-x^4+24x^3-206x^2+745x-962=0\)
\(\Leftrightarrow-\left(x^2-13x+37\right)\left(x^2-11x+26\right)=0\)
\(\Rightarrow x=-\frac{\sqrt{17}-11}{2}\) (thỏa)
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