Question

giải phương trình:

\(\sqrt{x+1}+\sqrt{3x}=3+\sqrt{4x-8}\)

Answer 1

Đk:\(x\ge2\)

PT \(\Leftrightarrow x+1+3x+2\sqrt{3x\left(x+1\right)}=9+4x-8+6\sqrt{4x-8}\)

\(\Leftrightarrow\sqrt{3x\left(x+1\right)}=3\sqrt{4x-8}\)

\(\Leftrightarrow3x\left(x+1\right)=9\left(4x-8\right)\)

\(\Leftrightarrow3x^2-33x+72=0\)

\(\Leftrightarrow3x^2-24x-9x+72=0\)

\(\Leftrightarrow\left(x-8\right)\left(3x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=3\end{matrix}\right.\)(Tm)

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