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Bandeano
@Bandeano
July 2022
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Log2(2x-1)-2=log2(x+2)-log2(x+1) Решите уравнение
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erzhan9210
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Одз 2х-1≥0
2х≥1
х≥1/2
х+2≥0
х≥-2
х+1≥0
х≥-1
log2(2x-1)-log2(4)=log2(x+2)-log2(x+1)
(2x-1)/4=(x+2)/(x+1)
(2x-1)(x+1)=4*(x+2)
2x²+2x-x-1=4x+8
2x²+x-1-4x-8=0
2x²-3x-9=0
D=9+4*2*9=9+72=81
x=(3±9)/4
x=12/4=3
x=-6/4=-1,5 не подходит одз
ответ х=3
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Answers & Comments
Verified answer
Одз 2х-1≥02х≥1
х≥1/2
х+2≥0
х≥-2
х+1≥0
х≥-1
log2(2x-1)-log2(4)=log2(x+2)-log2(x+1)
(2x-1)/4=(x+2)/(x+1)
(2x-1)(x+1)=4*(x+2)
2x²+2x-x-1=4x+8
2x²+x-1-4x-8=0
2x²-3x-9=0
D=9+4*2*9=9+72=81
x=(3±9)/4
x=12/4=3
x=-6/4=-1,5 не подходит одз
ответ х=3