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aivashkina
@aivashkina
July 2022
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Найдите корни уравнения log5(x-7)+log5(x-2)=log5(x+5)
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Kixcertborn2
Verified answer
log5(x-7)+log5(x-2)=log5(x+5)
Одз: x-7
≤0 x≤7
x-3≤0 x≤2 ===>>x∈(7, +∞)
x+5≤0 x≤-5
log5((x-7)*(x-2))=log5(x+5)
log(x^2-9x+14)=log5(x+5)
x^2-9x+14=x+5
x^2-9x+14-x-5=0
x^2-10x+9=0
D=(-10)^2-4*1*9=100-36=54=8^2
x=(10
±8)/2
x
₁=9
так как по одз x∈(7, +∞)====>>
x₂=1-не подходит
x₂=1
Ответ:x=9
1 votes
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Answers & Comments
Verified answer
log5(x-7)+log5(x-2)=log5(x+5)Одз: x-7≤0 x≤7
x-3≤0 x≤2 ===>>x∈(7, +∞)
x+5≤0 x≤-5
log5((x-7)*(x-2))=log5(x+5)
log(x^2-9x+14)=log5(x+5)
x^2-9x+14=x+5
x^2-9x+14-x-5=0
x^2-10x+9=0
D=(-10)^2-4*1*9=100-36=54=8^2
x=(10±8)/2
x₁=9
так как по одз x∈(7, +∞)====>>x₂=1-не подходит
x₂=1
Ответ:x=9