Question

Fie A multimia solutilor reale ale ecuatiei 3x²-2x-8=0.determinati multimia A/N

Answer 1

$3x^2-2x-8=0 \\ \\ \Delta = (-2)^2-4\cdot 3\cdot (-8) = 4+12\cdot 8 = 4+96 = 100 \\ \\ x_{1,2} = \dfrac{-(-2)\pm \sqrt{100}}{2\cdot 3} = \dfrac{2\pm 10}{6} \Rightarrow \left\| \begin{array}{ll} x_1 = \dfrac{2-10}{6} = -\dfrac{8}{6} = -\dfrac{4}{3} \\ \\ x_2 = \dfrac{2+10}{6} = \dfrac{12}{6} = 2 \end{array} \right | \\ \\ \Rightarrow A = \Big\{-\dfrac{4}{3},2\Big\} \Rightarrow \boxed{A \backslash \mathbb_{N} = \left\{-\dfrac{4}{3}\right\}}$