Question

Heeelp heeelp heeelp, ecuația de mai jos. Dau coroană!

Answer 1

Formule utilizate:

$\begin{vmatrix}a & b\\c & d \end{vmatrix} = ad - bc$

$\begin{vmatrix}a & b & c\\d & e & f \\ g & h & j \end{vmatrix} = a \begin{vmatrix} e & f \\ h & f\end{vmatrix} - b \begin{vmatrix} d & f \\ g & j\end{vmatrix} + c \begin{vmatrix} d & e\\ g & h\end{vmatrix}$

1)

$\begin{vmatrix} x & 2 \\ 5 & 2 \end{vmatrix} = 2x - 10 = 4 \implies \boxed{x = 7}$

2)

$\begin{vmatrix}2 & -6 & 4 \\ 5 & 7 & 10 \\ -1 & 3 & -2 \end{vmatrix} = 2 & \begin{vmatrix} 7 & 10 \\ 3 & -2\end{vmatrix} - (-6) \begin{vmatrix}5 & 10 \\ -1 & -2 \end{vmatrix} +4 \begin{vmatrix}5 & 7 \\ -1 & 3 \end{vmatrix} =\\ = 2 (-14 - 30) + 6(-10 + 10) + 4(15 + 7) = -88 + 0 + 88 = 0$

$x^{2} - 7x = 0\iff x(x-7) = 0 \implies \boxed{x_{1} = 0},\text{ } \boxed{x_{2} = 7}$