Question

a) tìm x, y, z biết:

\(\left(x-\frac{1}{5}\right).\left(y+\frac{1}{2}\right).\left(z-3\right)=0\)và \(x+1=y+2=z+3\)

b) Tìm x biết \(|x^2+|x-1||=x^2+2\)

Answer 1

a/ \(\left(x-\frac{1}{5}\right)\left(y+\frac{1}{2}\right)\left(z-3\right)=0\Rightarrow\left[{}\begin{matrix}x=\frac{1}{5}\\y=-\frac{1}{2}\\z=3\end{matrix}\right.\)

Với \(x=\frac{1}{5}\Rightarrow\left\{{}\begin{matrix}y=x-1=-\frac{4}{5}\\z=x-2=-\frac{9}{5}\end{matrix}\right.\)

Với \(y=-\frac{1}{2}\Rightarrow\left\{{}\begin{matrix}x=y+1=\frac{1}{2}\\z=y-1=-\frac{3}{2}\end{matrix}\right.\)

Với \(z=3\Rightarrow\left\{{}\begin{matrix}x=z+2=5\\y=z+1=4\end{matrix}\right.\)

b/ \(\Leftrightarrow x^2+\left|x-1\right|=x^2+2\)

\(\Leftrightarrow\left|x-1\right|=2\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)