Question

sa se arate ca numarul a= 3- 2 radical din 2 totul sub radical - 3 + 2 radical din 2 totul sub radical + 2 ∈ N

Answer 1

[tex]a = \sqrt{3-2\sqrt2} -\sqrt{3+2\sqrt2}+2\\ \\ a = \sqrt{(\sqrt2-1)^2} -\sqrt{(\sqrt2+1)^2} +2\\ \\ a = \big|\sqrt2-1\big| - \big|\sqrt2+1\big|+2 \\ \\ a = \sqrt2-1-(\sqrt2+1)+2 \\ \\ a = \sqrt2-1-\sqrt2-1+2 \\ \\ a = -2+2 \\ \\ a = 0 \in \mathbb_{N} [/tex]