Question

(x+3\(\sqrt{x}\)+2)(x+9\(\sqrt{x}\) +18)=168x

Answer 1

Đk:x\(\ge0\)

\(pt\Leftrightarrow\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)\left(\sqrt{x}+6\right)=168x\)

\(\Leftrightarrow\left(x+5\sqrt{x}+6\right)\left(x+7\sqrt{x}+6\right)=168x\)

\(\Leftrightarrow\left(x+6\sqrt{x}+6\right)^2=169x\)

\(\Leftrightarrow x+6\sqrt{x}+6=13\sqrt{x}\)

\(\Leftrightarrow x-7\sqrt{x}+6=0\)

\(\Leftrightarrow\begin{cases}\sqrt{x}=1\\\sqrt{x}=6\end{cases}\)\(\Leftrightarrow\begin{cases}x=1\\x=36\end{cases}\) (thỏa mãn)