Question

sabendo que det(e)= -76, calcule x
1    x   -3
4    5   -1
x   -3    1

Answer 1

[$\left[\begin{array}{ccc}1&x&-3\\4&5&-1\\x&-3&1\end{array}\right] \left[\begin{array}{cc}1&x\\4&5\\x&-3\end{array}\right] = -76 \\ 5-x^2+36-(-15x+3+4x)= -76 \\ 5-x^2+36+15x-3-4x=-76 \\ -x^2+11x+38+76=0 \\ -x^2+11x+114=0 \\ x= \dfrac{-b \pm \sqrt{b^2-4ac} }{2a} \\ x= \dfrac{-11\pm \sqrt{121-4 \cdot (-1) \cdot 114} }{2 \cdot (-1)} \\ x= \dfrac{-11\pm \sqrt{577} }{-2}\\ x_1= \dfrac{-11+ \sqrt{577} }{-2} ou x_2 = \dfrac{-11- \sqrt{577} }{-2}$