Giải bài 4.1 trang 198 - SBT Giải tích lớp 12
Tìm các số thực \(x, y\) thỏa mãn :
\(a) 2x+1+(1-2y)i=2-x+(3y-2)i\\ b) 4x+3+(3y-2)i=y+1+(x-3)i\\ c) x+2y+(2x-y)i=2x+y+(x+2y)i\)
Hướng dẫn:
\(a+bi=a'+b'i\Leftrightarrow \left\{ \begin{aligned} & a=a' \\ & b=b' \\ \end{aligned} \right. \)
a)
\(\left\{ \begin{aligned}
& 2x+1=2-x \\
& 1-2y=3y-2 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=\dfrac{1}{3} \\
& y=\dfrac{3}{5} \\
\end{aligned} \right.\)
b)
\(\left\{ \begin{aligned}
& 4x+3=y+1 \\
& 3y-2=x-3 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& 4x-y=-2 \\
& x-3y=1 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=-\dfrac{7}{11} \\
& y=-\dfrac{6}{11} \\
\end{aligned} \right. \)
c)
\(\left\{ \begin{aligned}
& x+2y=2x+y \\
& 2x-y=x+2y \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=-y \\
& x=y \\
\end{aligned} \right.\Leftrightarrow x=y=0 \)