Ta có \(\Delta'=b'^2-ac=\left(-3\right)^2-m=9-m\)
Để phương trình trên có 2 nghiệm thì \(\Delta'\ge0\Leftrightarrow9-m\ge0\Leftrightarrow m\le9\)
Áp dụng Viet, ta có: \(\left\{{}\begin{matrix}x_1+x_2=-\frac{b}{a}=6\\x_1x_2=m\end{matrix}\right.\)
a) Ta có:
\(x_1^2+x_2^2=36\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=36\\ \Leftrightarrow6^2-2m=36\Leftrightarrow2m=0\Leftrightarrow m=0\left(tm\right)\)
b) Ta có:
\(\frac{1}{x_1}+\frac{1}{x_2}=3\Leftrightarrow\frac{x_2+x_1}{x_1x_2}=3\Leftrightarrow\frac{6}{m}=3\Leftrightarrow m=2\left(tm\right)\)
c) Ta có:
\(\left\{{}\begin{matrix}x_1+x_2=6\\x_1-x_2=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x_1=10\\x_1-x_2=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x_1=5\\x_2=x_1-4=5-4=1\end{matrix}\right.\)
Thay x1; x2 vào x1x2=m, ta có:
\(5\cdot1=m\Leftrightarrow m=5\left(tm\right)\)
