Question

X²+(m-1)x+3=0;X1=3X2.

Answer 1

Răspuns:

m = -3; m = 5

Explicație pas cu pas:

$\left\{\begin{array}{c}x_{1}+x_{2} = -(m-1) \\ x_{1}x_{2} = 3 \\ x_{1} = 3x_{2} \end{array}\right. < = > \left\{\begin{array}{c}x_{1}+x_{2} = 1 - m \\ 3x_{2}\cdot x_{2} = 3 \\ x_{1} = 3x_{2} \end{array}\right.$

$\left\{\begin{array}{c}x_{1}+x_{2} = 1 - m\\ {(x_{2})}^{2} = 1 \\ x_{1} = 3x_{2} \end{array}\right.$

I.

$\left\{\begin{array}{c} - 4 = 1 - m \\ {x_{2}} = - 1 \\ x_{1} = - 3 \end{array}\right. = > \left\{\begin{array}{c} m = 5 \\ {x_{2}} = - 1 \\ x_{1} = - 3 \end{array}\right.$

II.

$\left\{\begin{array}{c} 4 = 1 - m \\ {x_{2}} = 1 \\ x_{1} = 3 \end{array}\right. = > \left\{\begin{array}{c} m = - 3 \\ {x_{2}} = 1 \\ x_{1} = 3 \end{array}\right.$