lg(x²+2x-7)-lg(x-1)=0 Пожалуйста подробно,пошаговой!. Created by Flover98. algebra-ru

lg(x²+2x-7)-lg(x-1)=0 Пожалуйста подробно,пошаговой!...

Flover98 @Flover98

August 2022 1 22 Report

lg(x²+2x-7)-lg(x-1)=0 Пожалуйста подробно,пошаговой!

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sangers1959

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Lg(x²+2x-7)-lg(x-1)=0
ОДЗ: x-1>0 x>1   x²+2x-7>0 x>-1+/-2√2 ⇒ x>-1+2√2≈1,82
lg((x²+2x-7)/(x-1))=0
(x²+2x-7)/(x-1)=10⁰
(x²+2x-7)/(x-1)=1
x²+2x-7=x-1
x²+x-6=0  D=25   √D=5
x₁=(-1+5)/2=2 x∈
x₂=(-1-5)/2=-3 x∉
Ответ: х=2.

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