Решите уравнение: log₆(x²-x)=1 . Created by elizavetadonch. matematika-ru

Решите уравнение: log₆(x²-x)=1 ...

elizavetadonch @elizavetadonch

July 2022 2 4 Report

Решите уравнение:
log₆(x²-x)=1

Lesben X(x-1)>0⇒x<0 U x>1
x²-x=6
x²-x-6=0
x1+x2=1 U x1*x2=-6
x1=-2 U x2=3

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sedinalana

Verified answer

Log6 (x²-x)=1 , x²-x bolše čem 0, x(x-1) bolše čem 0
x bolše čem 1 ∨ x menše čem 0
x∈(-∞,0)∪(1,∞)
x²-x= 6ˇ1
x²-x=6
x²-x-6=0, D=1+24=25, √D=√25=5
x1=(1+5)/2=6/2=3
x2=(1-5)/2=-4/2=-2
Otvet: x= 3 ∨ x=-2

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