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Мирабелль
@Мирабелль
August 2022
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log^x+1(x-1/2) = log^x-1/2 (x+1)
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Answers & Comments
pomoshnik09
условимся : рядом логарифмом пишу основание потом число
log(x+1) (x-1/2)=1/log(x+1) (x-1/2)
log(x+1) (x-1/2)-1/log(x+1) (x-1/2)=0
(log²(x+1) (x-1/2)-1=0. log(x+1) (x-1/2)≠0
(log(x+1) (x-1/2)-1)*(log(x+1) (x-1/2)+1)=0. x>1/2. x≠3/2
log(x+1) (x-1/2)-1=0 или log(x+1) (x-1/2)+1=0
log(x+1) (x-1/2)=1 log(x+1) (x-1/2)=-1
x+1=x-1/2 x-1/2=1/(x+1)
нет решения (x-1/2)(x+1)-1=0
x²-1/2x+x-1/2-1=0
x²+1/2x-3/2=0 /*2
2x²+x-3=0 D=1²-4*2*-3=25
x1=-1+5)/4=4/4=1 x2=-1-5)/4=-6/4=-3/2
-3/2-постороний корень
ответ 1
2 votes
Thanks 1
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Answers & Comments
log(x+1) (x-1/2)=1/log(x+1) (x-1/2)
log(x+1) (x-1/2)-1/log(x+1) (x-1/2)=0
(log²(x+1) (x-1/2)-1=0. log(x+1) (x-1/2)≠0
(log(x+1) (x-1/2)-1)*(log(x+1) (x-1/2)+1)=0. x>1/2. x≠3/2
log(x+1) (x-1/2)-1=0 или log(x+1) (x-1/2)+1=0
log(x+1) (x-1/2)=1 log(x+1) (x-1/2)=-1
x+1=x-1/2 x-1/2=1/(x+1)
нет решения (x-1/2)(x+1)-1=0
x²-1/2x+x-1/2-1=0
x²+1/2x-3/2=0 /*2
2x²+x-3=0 D=1²-4*2*-3=25
x1=-1+5)/4=4/4=1 x2=-1-5)/4=-6/4=-3/2
-3/2-постороний корень
ответ 1