Question

Calculati suma elementelor multimii A={x apartine R/(x-1)la a doua(2)=3 Sau pe scurt clasa a 7.A pagina 188 Varianta 2 Sub.2 ex. 4a cartea editura,,Clubul Matematicienilor"

Answer 1

   
[tex]\displaystyle \\ A = \{ x \in R | (x-1)^2 = 3\} \\ \texttt{Rezolvam ecuatia: } \\ (x-1)^2 = 3 \\ x^2 -2x + 1 = 3 \\ x^2 -2x + 1 - 3 = 0 \\ x^2 -2x -2 = 0 \\ \\ x_{12}= \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{2 \pm \sqrt{4 +8} }{2} = \frac{2 \pm 2\sqrt{3} }{2} = 1 \pm \sqrt{3} \\ \\ x_1 = \boxed{1 + \sqrt{3} }\\ x_2 = \boxed{1 - \sqrt{3} }\\ \\ A = \{ 1 + \sqrt{3}, ~1 - \sqrt{3} \} \\ \\ \boxed{S = 1 + \sqrt{3} + 1 - \sqrt{3} = 1+1 = 2 }[/tex]