Să se rezolve în mulţime numerelor reale ecuaţia : radical de ordin 3 din ( x^2 − x − 3 )= −1.
albastruverde12
![\sqrt[3]{x^2-x-3}=-1 \\ \\ Ridicam~la~cub~si~obtinem: \\ \\ x^2-x-3=-1 \\ \\ x^2-x-2=0 \\ \\ \Delta=(-1)^2-4 \cdot 1 \cdot (-2)=9 \\ \\ x_{1,2}= \frac{1 \pm \sqrt { \Delta}}{2}= \frac{1 \pm 3}{2} = \left \{ {{-1} \atop {2}} \right. . \\ \\ \underline{Solutie}: x \in \{-1;2\}.](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7Bx%5E2-x-3%7D%3D-1+%5C%5C++%5C%5C+Ridicam%7Ela%7Ecub%7Esi%7Eobtinem%3A++%5C%5C++%5C%5C+x%5E2-x-3%3D-1+%5C%5C++%5C%5C+x%5E2-x-2%3D0+%5C%5C++%5C%5C+%5CDelta%3D%28-1%29%5E2-4+%5Ccdot+1+%5Ccdot+%28-2%29%3D9+%5C%5C++%5C%5C+x_%7B1%2C2%7D%3D+%5Cfrac%7B1+%5Cpm+%5Csqrt+%7B+%5CDelta%7D%7D%7B2%7D%3D+++%5Cfrac%7B1+%5Cpm+3%7D%7B2%7D++%3D+%5Cleft+%5C%7B+%7B%7B-1%7D+%5Catop+%7B2%7D%7D+%5Cright.+.+%5C%5C++%5C%5C+%5Cunderline%7BSolutie%7D%3A+x+%5Cin+%5C%7B-1%3B2%5C%7D.+++ "\sqrt[3]{x^2-x-3}=-1 \\ \\ Ridicam~la~cub~si~obtinem: \\ \\ x^2-x-3=-1 \\ \\ x^2-x-2=0 \\ \\ \Delta=(-1)^2-4 \cdot 1 \cdot (-2)=9 \\ \\ x_{1,2}= \frac{1 \pm \sqrt { \Delta}}{2}= \frac{1 \pm 3}{2} = \left \{ {{-1} \atop {2}} \right. . \\ \\ \underline{Solutie}: x \in \{-1;2\}.")
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