Question

Giải các phương trình sau. √x²-6x+9=4-x. √x²-10x+25=3-19x. √x²-9+√x²-6x+9=0. √2x-2+2√2x-3+√2x+13+8√2x-3=5

Answer 1

a: =>|x-3|=4-x

\(\Leftrightarrow\left\{{}\begin{matrix}x< =4\\\left(4-x-x+3\right)\left(4-x+x-3\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =4\\\left(7-2x\right)=0\end{matrix}\right.\Leftrightarrow x=\dfrac{7}{2}\)

b: =>|x-5|=3-19x

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{19}\\\left(x-5-3+19x\right)\left(x-5+3-19x\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{19}\\\left(20x-8\right)\left(-18x-2\right)=0\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{1}{9}\right\}\)

c: =>\(\Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}+\sqrt{x-3}\right)=0\)

=>căn x-3=0

=>x=3