Помогите пжл неравенство решить. Created by Delya08. algebra-ru

Помогите пжл неравенство решить...

Delya08 @Delya08

July 2022 1 6 Report

Помогите пжл неравенство решить

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sangers1959

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(x²-5x+4)/log₂(x-1)≥0
x²-5x+4=x²-x-4x+4=x(x-1)-4(x-1)=(x-4)(x-1) ⇒
(x-1)(x-4)/log₂(x-1)≥0
x-1>0 x>1
x-4≥0 x≥4
log₂(x-1)>0 x-1>2⁰ x-1>1 x>2 ⇒ x∈[4;+∞)

x-1>0 x>1
x-4≤0 x≤4
log₂(x-1)<0 x-1<2⁰ x-1<1 x<2 ⇒ x∈(1;2)
Ответ: х∈(1;2)U[4;+∞).

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