Question

puteti sa ma ajutati va rog mult cu acea expresie?​

Answer 1

E(x) e constantă dacă nu depinde de x.

$\\E(x) =\sqrt{x^2-2\sqrt 2 x+2}+|x-\sqrt 3|+\sqrt 2 \\ \\\Rightarrow E(x) = \sqrt{(x-\sqrt 2)^2}+|x-\sqrt 3|+\sqrt 2 \\ \\\Rightarrow E(x) = |x-\sqrt 2| + |x-\sqrt 3|+\sqrt 2\\\\ \\ x\in [\sqrt 2,\sqrt 3] \Rightarrow \begin{cases}x-\sqrt 2 \geq 0 \Rightarrow |x-\sqrt 2| = +(x-\sqrt 2)\\ x-\sqrt 3 \leq 0 \Rightarrow |x-\sqrt 3| = -(x-\sqrt 3)\end{cases}\\ \\\\ \Rightarrow E(x) = (x-\sqrt 2) -(x-\sqrt 3)+\sqrt 2 \\ \\ \Rightarrow E(x) = x-\sqrt 2 - x+\sqrt 3+\sqrt 2 \\ \\ \Rightarrow E(x) = \sqrt 3,\quad \forall x\in [\sqrt 2,\sqrt 3]$