a, Để pt có nghiệm thì \(\Delta\ge0\)
Hay: \(\left(-3\right)^2-4\left(m-1\right)\ge0\)
\(\Leftrightarrow9-4m+4\ge0\)
\(\Leftrightarrow-4m\ge-13\)
\(\Leftrightarrow m\le\frac{13}{4}\)
b, Với \(m\le\frac{13}{4}\), theo Vi-ét, ta có: \(\hept{\begin{cases}x_1+x_2=3\\x_1x_2=m-1\end{cases}}\)
Ta có: \(x_1^2-x_2^2=15\)
\(\Leftrightarrow\left(x_1+x_2\right)\left(x_1-x_2\right)=15\)
\(\Leftrightarrow\left(x_1+x_2\right)\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}=15\)
\(\Leftrightarrow3\sqrt{3^2-4\left(m-1\right)}=15\)
\(\Leftrightarrow\sqrt{9-4m+4}=5\)
\(\Leftrightarrow\sqrt{13-4m}=5\)
\(\Leftrightarrow13-4m=25\)
\(\Leftrightarrow4m=-12\)
\(\Leftrightarrow m=-3\left(tm\right)\)
=.= hk tốt!!