Question

x² + \(\sqrt{x^2-10x+9}\) = 10x + 3

Answer 1

Đặt \(\sqrt{x^2-10x+9}=t\left(t\ge0\right)\)

\(\Leftrightarrow x^2-10x+9=t^2\)

\(pt\Leftrightarrow x^2-10x-3+\sqrt{x^2-10x+9}=0\)

\(\Leftrightarrow t^2+t-12=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t=-4\left(loai\right)\\t=3\end{matrix}\right.\)

Với t=3\(\Leftrightarrow x^2-10x+9=9\)

\(\Leftrightarrow x\left(x-10\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=10\end{matrix}\right.\)