Question

Помогите мне решить Задачу!

Answer 1

ОДЗ: a² - a ≥ 0 ∩ a² - 1 ≥ 0 ∩ 2 - 2a > 0

a·(a - 1) ≥ 0 ∩ (a - 1)(a + 1) ≥ 0 ∩ a < 1

(a ∈ (-∞; 0) ∪ (1; +∞)) ∩ (a ∈ (-∞; -1) ∪ (1; +∞)) ∩ (a ∈ (-∞; 1))

a < -1

$frac{sqrt{a^2-a}+sqrt{a^2-1}}{sqrt{2-2a}}=frac{sqrt{-a(1-a)}+sqrt{-(1+a)(1-a)}}{sqrt{2(1-a)}}=frac{sqrt{1-a}(sqrt{-a}+sqrt{-(1+a)})}{sqrt{1-a}sqrt{2}}=frac{sqrt{-a}+sqrt{-(1+a)}}{sqrt{2}}$