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alovosiem
@alovosiem
July 2022
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помогите, срочно, плииииз! я затупила! не получается доделать!
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sangers1959
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(lg8-lg(x-5))/(lg√((x+7)-lg2)=-1 ОДЗ: x-5>0 x>5 x+7>0 x>-7 ⇒ x∈(5;+∞)
lg(8/(x-5))=-lg(√(x+7)/2)
lg(8/(x-5))=lg(√(x+7)/2)⁻¹
8/(x-5)=2/√(x+7) |÷2
4/(x-5)=1/√(x+7)
4*√(x+7)=x-5
(4*√(x+7))²=(x-5)²
16*(x+7)=x²-10x+25
16x+112=x²-10x+25
x²-26x-87=0 D=196
x=29 x=-3∉ОДЗ
Ответ: x=29.
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Answers & Comments
Verified answer
(lg8-lg(x-5))/(lg√((x+7)-lg2)=-1 ОДЗ: x-5>0 x>5 x+7>0 x>-7 ⇒ x∈(5;+∞)lg(8/(x-5))=-lg(√(x+7)/2)
lg(8/(x-5))=lg(√(x+7)/2)⁻¹
8/(x-5)=2/√(x+7) |÷2
4/(x-5)=1/√(x+7)
4*√(x+7)=x-5
(4*√(x+7))²=(x-5)²
16*(x+7)=x²-10x+25
16x+112=x²-10x+25
x²-26x-87=0 D=196
x=29 x=-3∉ОДЗ
Ответ: x=29.