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SenyaSavochkin111
@SenyaSavochkin111
August 2022
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50 баллов один пример
log0,5(2x-3)+2=-log0,5(x+2)
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Evgenia4836
Verified answer
ОДЗ: 2x-3>0, x>1.5
x+2>0, x>-2
log0,5(2x-3)+log0,5(x+2)=-2
log0.5(2x²+4x-3x-6)=-2
log0.5(2x²+x-6)=-2
2x²+x-6=(0.5)^-2
2x²+x-6=2²
2x²+x-6-4=0
2x²+x-10=0
D=1+80=81
x1=(-1+9)/4=2
x2=(-1-9)/4= -5/2 не корень по ОДЗ
ответ: x=2
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Answers & Comments
Verified answer
ОДЗ: 2x-3>0, x>1.5x+2>0, x>-2
log0,5(2x-3)+log0,5(x+2)=-2
log0.5(2x²+4x-3x-6)=-2
log0.5(2x²+x-6)=-2
2x²+x-6=(0.5)^-2
2x²+x-6=2²
2x²+x-6-4=0
2x²+x-10=0
D=1+80=81
x1=(-1+9)/4=2
x2=(-1-9)/4= -5/2 не корень по ОДЗ
ответ: x=2