Question

Bài 1.

a) \(\sqrt{4x^2}=x+1\) b) \(\sqrt{16x^2}=8\)

c) \(\sqrt{1-2x}+x^2=3\) d) \(\sqrt{x^2+6x+9}=x-1\)

e) \(\sqrt{x^2+4x+4}-2=x\) f) \(1-\sqrt{4x^2-4x+1}=2x\)

GIÚP MÌNH VỚI MỌI NGƯỜI ƠI!!!!!!!

Answer 1

a) \(\sqrt{4x^2}=x+1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1\ge0\\4x^2=\left(x+1\right)^2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\4x^2=x^2+2x+1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\3x^2-2x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\\left(3x+1\right)\left(x-1\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\\left[{}\begin{matrix}x=-\frac{1}{3}\\x=1\end{matrix}\right.\left(TM\right)\end{matrix}\right.\)

b) \(\sqrt{16x^2}=8\Leftrightarrow16x^2=64\)

\(\Leftrightarrow x^2=4\Leftrightarrow x=\pm2\) ( TM )