Question

Care sunt solutiile ecuatiei: X^3+3=0 ?

Answer 1

Buna!

x³ + 3 = 0
x³ = -3
x = ³√-3

Bafta :)

Answer 2

$x^3+3=0 \Rightarrow x^3 + \sqrt[3]{3}^3 = 0 \Rightarrow (x+ \sqrt[3]{3})(x^2-x \sqrt[3]{3}+ \sqrt[3]{3}^2) = 0 \\ \\ \boxed{1} \quad x+ \sqrt[3]{3} = 0 \Rightarrow x = - \sqrt[3]{3} \\ \\ \boxed{2} \quad x^2-x \sqrt[3]{3}+ \sqrt[3]{3}^2 =0 \\ \Delta = \sqrt[3]{3}^2-4\sqrt[3]{3}^2 = -3\sqrt[3]{3}^2 \Rightarrow x_{1,2} = \dfrac{\sqrt[3]{3}\pm \sqrt{3\sqrt[3]{3}^2}i }{2} \Rightarrow$

$\Rightarrow x_{1,2}= \dfrac{\sqrt[3]{3}\pm\sqrt[3]{3} \cdot\sqrt{3}i }{2} \Rightarrow x_{1,2} = \dfrac{\sqrt[3]{3}\pm\sqrt[3+2]{3} i }{2} \Rightarrow x_{1,2} = \dfrac{\sqrt[3]{3}\pm\sqrt[5]{3} i }{2} \\ \\ \\ Din \boxed{1} \cup \boxed{2} \Rightarrow S = \left\{\sqrt[3]{-3}; \dfrac{\sqrt[3]{3}}{2}-\dfrac{\sqrt[5]{3} }{2}i; \dfrac{\sqrt[3]{3}}{2}+\dfrac{\sqrt[5]{3} }{2}i \right\}$