sabendo que det(e)= -76, calcule x
1 x -3
4 5 -1
x -3 1
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[![\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}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3Bx%26amp%3B-3%5C%5C4%26amp%3B5%26amp%3B-1%5C%5Cx%26amp%3B-3%26amp%3B1%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26amp%3Bx%5C%5C4%26amp%3B5%5C%5Cx%26amp%3B-3%5Cend%7Barray%7D%5Cright%5D+%3D+-76+%5C%5C+5-x%5E2%2B36-%28-15x%2B3%2B4x%29%3D+-76+%5C%5C+5-x%5E2%2B36%2B15x-3-4x%3D-76+%5C%5C+-x%5E2%2B11x%2B38%2B76%3D0+%5C%5C+-x%5E2%2B11x%2B114%3D0+%5C%5C+x%3D+%5Cdfrac%7B-b+%5Cpm+%5Csqrt%7Bb%5E2-4ac%7D+%7D%7B2a%7D+%5C%5C+x%3D+%5Cdfrac%7B-11%5Cpm+%5Csqrt%7B121-4+%5Ccdot+%28-1%29+%5Ccdot+114%7D+%7D%7B2+%5Ccdot+%28-1%29%7D+%5C%5C+x%3D+%5Cdfrac%7B-11%5Cpm+%5Csqrt%7B577%7D+%7D%7B-2%7D%5C%5C%0Ax_1%3D+%5Cdfrac%7B-11%2B+%5Csqrt%7B577%7D+%7D%7B-2%7D+%24++ou++%24+x_2+%3D+%5Cdfrac%7B-11-+%5Csqrt%7B577%7D+%7D%7B-2%7D+ "\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}")
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