Question

$\sqrt[3]{} x^{3}+1$=x+1

Ajutor , va rog :D

Answer 1

$\sqrt[3]{x^3+1} = x+1\Big|^3 \Rightarrow \\ \Rightarrow \Big(\sqrt[3]{x^3+1}\Big)^3 = \big(x+1\big)^3 \Rightarrow \\ \Rightarrow x^3+1 = x^3+3\cdot x\cdot1^2+3\cdot x^2\cdot 1 + 1^3 \Rightarrow \\ \Rightarrow x^3 +1 = x^3+3x^2+3x+1 \Rightarrow3x^2+3x=0 \Rightarrow 3x(x+1) = 0 \\ \Rightarrow x_1=0, \quad x_2=-1 \Rightarrow S = \Big\{-1,0\Big\}$