Question

với giá trị nào của x thì \(\sqrt{x^2-5x+4}\) có nghĩa

Answer 1

\(\sqrt{x^2-5x+4}\)có nghĩa\(\Leftrightarrow x^2-5x+4\ge0\Leftrightarrow x^2-4x-x+4\ge0\Leftrightarrow x\cdot\left(x-4\right)-\left(x-4\right)\ge0\Leftrightarrow\left(x-4\right)\cdot\left(x-1\right)\ge0\Leftrightarrow\left\{{}\begin{matrix}x-4\ge0\\x-1\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\x\ge1\end{matrix}\right.\Leftrightarrow x\ge4\)

Answer 2

Để \(\sqrt{x^2-5x+4}\) có nghĩa thì:

\(x^2-5x+4\ge0\)

\(\Leftrightarrow\left(x-\dfrac{5}{2}\right)^2-\dfrac{5}{2}\ge0\)

\(\Leftrightarrow\left(x-\dfrac{5}{2}\right)^2\ge\dfrac{5}{2}\) \(\Leftrightarrow x-\dfrac{5}{2}\ge\dfrac{\sqrt{5}}{\sqrt{2}}\)

\(\Leftrightarrow x\ge\dfrac{\sqrt{10}+5}{2}\)