Question

x este un număr real, x nu este 0 si 2. Arătați ca E(x)= 1-1/x, pentru orice x număr real, x nu este 0 si 2​

Answer 1

$E(x) = \Bigg(\dfrac{x^3-2x^2}{2x^2}-\dfrac{x^2-4}{4x}\Bigg):\dfrac{x-2}{2}+\dfrac{1}{2} \\ \\ E(x) = \Bigg(\dfrac{x^2(x-2)}{2x^2}-\dfrac{(x-2)(x+2)}{4x}\Bigg):\dfrac{x-2}{2}+\dfrac{1}{2} \\ \\E(x) = \Bigg(\dfrac{x-2}{2}:\dfrac{x-2}{2}-\dfrac{(x-2)(x+2)}{4x}:\dfrac{x-2}{2}\Bigg)+\dfrac{1}{2}$

$E(x) = \Bigg(\dfrac{1}{1} - \dfrac{x+2}{2x}\Bigg)+\dfrac{1}{2}\\ \\ E(x) = 1 +\dfrac{1}{2} - \dfrac{x+2}{2x} \\ \\ E(x) =1+\dfrac{x-(x+2)}{2x}\\ \\ E(x) = 1+\dfrac{-2}{2x} \\ \\ \boxed{E(x) = 1-\dfrac{1}{x},\quad\forall x\in\mathbb{R}\backslash \{0,2\}}$

Answer 2

Răspuns:

Explicație pas cu pas: