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DashaMedvedkova
@DashaMedvedkova
August 2022
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Решите 1/2 lg(2x-1)=1-lg√x-9
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sangers1959
Verified answer
(1/2)*lg(2x-1)=1-lg√(x-9)
ОДЗ: 2x-1>0 x>0,5 x-9>0 x>9 ⇒ x∈(9;+∞)
lg√(2x-1)+lg√(x-9)=1
lg√((2x-1)(x-9))=lg10
√((2x-1)(x-9))=10
2x²-19x+9=100
2x²-19x-91=0 D=1089
x₁=13 x₂=-3,5 ∉ОДЗ≈
Ответ: х=13.
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Answers & Comments
Verified answer
(1/2)*lg(2x-1)=1-lg√(x-9)ОДЗ: 2x-1>0 x>0,5 x-9>0 x>9 ⇒ x∈(9;+∞)
lg√(2x-1)+lg√(x-9)=1
lg√((2x-1)(x-9))=lg10
√((2x-1)(x-9))=10
2x²-19x+9=100
2x²-19x-91=0 D=1089
x₁=13 x₂=-3,5 ∉ОДЗ≈
Ответ: х=13.