Bài 1:
a) Pt: \(x^2-3mx-m-16=0\)
\(\Delta=\left(-3m\right)^2-4\cdot1\cdot\left(-m-16\right)\)
\(=9m^2+4m+64\)
\(=\left(9m^2+2\cdot3m\cdot\dfrac{2}{3}+\dfrac{4}{9}\right)+\left(64-\dfrac{4}{9}\right)\)
\(=\left(3m+\dfrac{2}{3}\right)^2+\dfrac{572}{9}>0\forall m\)
Hay phương trình có nghiệm với mọi m
b) Theo vi-ét: \(\left\{{}\begin{matrix}x_1x_2=-m-16\\x_1+x_2=3m\end{matrix}\right.\)
\(\left(x_1-x_2\right)^2=0\)
\(\Leftrightarrow x_1^2-2x_1x_2+x^2_2=0\)
\(\Leftrightarrow\left(x_1^2+x_2^2\right)-2x_1x_2=0\)
\(\Leftrightarrow\left[\left(x_1+x_2\right)^2-2x_1x_2\right]-2x_1x_2=0\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-4x_1x_2=0\)
\(\Rightarrow\left(3m\right)^2-4\left(-m-16\right)=0\)
\(\Leftrightarrow9m^2+4m+64=0\)
\(\Leftrightarrow\left(3m+\dfrac{2}{3}\right)^2+\dfrac{572}{9}>0\forall m\)
Không có m thỏa mãn
