cho a/b=3/b=b/a.Chung minh :a=b(voi a+b khong= -3) 19/09/2021 Bởi Margaret cho a/b=3/b=b/a.Chung minh :a=b(voi a+b khong= -3)
\[\begin{array}{l} \frac{a}{b} = \frac{3}{b} = \frac{b}{a}\,\,\left( {a,\,b \ne 0} \right) \Rightarrow \left\{ \begin{array}{l} ab = 3b\\ {b^2} = 3a \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} a = \frac{{{b^2}}}{3}\\ \frac{{{b^2}}}{3}.b = 3b \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} a = \frac{{{b^2}}}{3}\\ {b^2} = 9 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} a = \frac{{{b^2}}}{3}\\ \left[ \begin{array}{l} b = 3\\ b = – 3 \end{array} \right. \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} a = \frac{9}{3} = 3\\ \left[ \begin{array}{l} b = 3\\ b = – 3 \end{array} \right. \end{array} \right. \Leftrightarrow b = a = 3. \end{array}\] Bình luận
\[\begin{array}{l}
\frac{a}{b} = \frac{3}{b} = \frac{b}{a}\,\,\left( {a,\,b \ne 0} \right) \Rightarrow \left\{ \begin{array}{l}
ab = 3b\\
{b^2} = 3a
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{3}\\
\frac{{{b^2}}}{3}.b = 3b
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{3}\\
{b^2} = 9
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{{{b^2}}}{3}\\
\left[ \begin{array}{l}
b = 3\\
b = – 3
\end{array} \right.
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = \frac{9}{3} = 3\\
\left[ \begin{array}{l}
b = 3\\
b = – 3
\end{array} \right.
\end{array} \right. \Leftrightarrow b = a = 3.
\end{array}\]