Question

Giải phương trình.

Answer 1

\(7-2x=\sqrt{x^2-10x+25}\left(đk:x\le\dfrac{7}{2}\right)\)

\(\Leftrightarrow7-2x=\sqrt{\left(x-5\right)^2}\)

\(\Leftrightarrow7-2x=\left|x-5\right|\)

\(\Leftrightarrow x-5=2x-7\)( do \(x\le\dfrac{7}{2}\Leftrightarrow x-5\le-\dfrac{3}{2}< 0\))

\(\Leftrightarrow x=2\left(tm\right)\)

Answer 2

\(ĐK:x\in R\\ PT\Leftrightarrow49-28x+4x^2=x^2-10x+25\\ \Leftrightarrow3x^2-18x+24=0\\ \Leftrightarrow3\left(x-4\right)\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)