Xet ptrinh $x^2 + 2x + m-1=0$
Co $\Delta' = 1^2 -(m-1) = m+2$
De ptrinh co 2 nghiem thi $\Delta'>0$ hay $m > -2$.
Khi do, ta co 2 nghiem la
$$x_1 = -1-\sqrt{m+2}, x_2 = -1+\sqrt{m+2}.$$
a) $x_1 - 3x_2 = -10$
Thay vao ta co
$-1-\sqrt{m+2} - 3(-1 + \sqrt{m+2}) = -10$
<->$ 4\sqrt{m+2} = 12$
<->$ \sqrt{m+2} = 3$
<-> $m+2 = 9$
<-> $m = 7$.
Vay $m=7$.
b) $2x_1 - 7x_2 = 12$
Thay vao ta co
$2(-1+\sqrt{m+2}) - 7(-1 - \sqrt{m+2}) = 12$
<->$ 9\sqrt{m+2} = 7$
<-> $\sqrt{m+2} = 7/9$
<->$ m+2 = 49/81$
<->$ m = -113/81 > -2$
Vay $m = -113/81$.
