a)\(\sqrt{3x+2}=2-\sqrt{3}\)
\(\Leftrightarrow3x+2=\left(2-\sqrt{3}\right)^2\)
\(\Leftrightarrow3x+2=7-4\sqrt{3}\)
\(\Leftrightarrow3x=7-2-4\sqrt{3}\)
\(\Leftrightarrow3x=5-4\sqrt{3}\)
\(\Leftrightarrow x=\dfrac{5}{3}-\dfrac{4\sqrt{3}}{3}\)
\(\Leftrightarrow x=\dfrac{5-4\sqrt{3}}{3}\)
b) \(\sqrt{x^2-4x+4}=49\)
\(\Leftrightarrow\sqrt{\left(x-2\right)^2}=49\)
\(\Leftrightarrow\left|x-2\right|=49\)\
\(\Leftrightarrow\left[{}\begin{matrix}x-2=49\\-x+2=49\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=51\\x=-47\end{matrix}\right.\)
c) \(\sqrt{x+1}=x-1\)
ĐKXĐ: \(x-1\ge0\Rightarrow x\ge1\)
\(\Leftrightarrow x+1=\left(x-1\right)^2\)
\(\Leftrightarrow x+1=x^2-2x+1\)
\(\Leftrightarrow-x^2+2x+x=-1+1\)
\(\Leftrightarrow3x-x^2=0\)
\(\Leftrightarrow x\left(3-x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(lo\text{ại}\right)\\x=3\left(nh\text{ậ}n\right)\end{matrix}\right.\)
d)e) lát mình làm sau
