Đáp án:
PT có 2 nghiệm phân biệt
$\rm ⇔\Delta>0\\⇔9-4(m-1)>0\\⇔4(m-1)<9\\⇔m<\dfrac{13}{4}$
Áp dụng vi-ét:
$\rm \begin{cases}x_1+x_2=3(1)\\x_1.x_2=m-1(2)\end{cases}$
$\rm x_1^2-x_2^2=50\\⇔(x_1-x_2)(x_1+x_2)=50⇔x_1-x_2=\dfrac{50}{3}\\⇔x_1=x_2+\dfrac{50}{3}$
Thay $\rm x_1=x_2+\dfrac{50}{3}$ vào (1) ta có:
$\rm 2x_2+\dfrac{50}{3}=3\\⇔2x_2=\dfrac{-41}{3}\\⇔x_2=\dfrac{-41}{6}\\⇔x_1=\dfrac{59}{6}$
Thay $\rm x_1=\dfrac{59}{6},x_2=\dfrac{-41}{6}$ vào (2) ta có:
$\rm m-1=\dfrac{-2419}{36}⇔m=\dfrac{-2383}{36}(tm)$
