произведение корней уравнения. Created by Infinity167. matematika-ru

произведение корней уравнения...

Infinity167 @Infinity167

August 2022 1 5 Report

произведение корней уравнения

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Санечка69

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(х² + х - 2)(х² + х + 2) = -2
Обозначим у = х² + х - 2, тогда получим уравнение:
у · (у + 4) = -2
у² + 4у + 2 = 0
D = 4² - 4 · 1 · 2 = 16 - 8 = 8; √8 = 2√2
y₁ = ( -4 - 2√2)/2 = -2 - √2
y₂ = (-4 + 2√2)/2√ = -2 + √2

х² + х - 2 = -2 - √2
х² + х - 2 + 2 + √2 = 0
х² + х + √2 = 0
D = 1² - 4 · 1 · √2 = 1 - 4√2< 0 - нет решений

х² + х - 2 = -2 + √2
х² + х - 2 + 2 - √2 = 0
х² + х - √2 = 0
D = 1² - 4 · 1 · (-√2) = 1 + 4√2 > 0
x₁₂ = (-1 +-√(1 + 4√2))/2

x₁ · x₂ = (-1 + √(1 + 4√2))/2 · (-1 - √(1 + 4√2))/2 =(1 - (√(1 + 4√2))²)/4 = (1 - 1 -4√2)/4 = (-4√2)/4 = -√2

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