Помогите мне решить Задачу!. Created by egormnovik. matematika-ru

Помогите мне решить Задачу!...

egormnovik @egormnovik

August 2022 1 4 Report

Помогите мне решить Задачу!

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flsh

Verified answer

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

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

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