Question

Rezolvati ecuatia:
x^2 + 2x + 1 = 3 + 2 radical din 2

Answer 1

[tex]x^2+2x+1 = 3+2\sqrt 2\\ \\ (x+1)^2 = 3+2\sqrt 2\Big|\sqrt{} \\ \\ \sqrt{(x+1)^2} = \sqrt{3+2\sqrt 2} \\ \\ |x+1| = \sqrt{(1+\sqrt 2)^2} \\ \\ |x+1| = |1+\sqrt 2| \\ \\ \boxed{1} \quad x+1 = 1+\sqrt 2 \Rightarrow x = 1-1+\sqrt 2 \Rightarrow x = \sqrt 2 \\ \\ \boxed{2}\quad x + 1 = -(1+\sqrt 2) \Rightarrow x + 1 = -1-\sqrt 2 \Rightarrow x = -2-\sqrt 2 \\ \\ \Rightarrow \boxed{S = \Big\{-2-\sqrt 2, \sqrt 2\Big\}}[/tex]