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iRandy
@iRandy
August 2022
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okneret
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Применены свойства логарифмов
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sangers1959
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4^(1+log₄(x+y)=12 4*4^log₄(x+y)=12 I÷4 4^log₄(x+y)=3 x+y=3
log₁/₃(x+y)+log₁/₃(x-y)=-1 log₁/₃(x²-y²)=log₁/₃3 x²-y²=3 ⇒
x+y=3 y=3-x
x²-y²=3 x²-(3-x)²=3 x²-9+6x-x²=3 6x=12 x=2 ⇒ y=3-2=1.
Ответ: x=2 y=1.
1 votes
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Answers & Comments
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Применены свойства логарифмовVerified answer
4^(1+log₄(x+y)=12 4*4^log₄(x+y)=12 I÷4 4^log₄(x+y)=3 x+y=3log₁/₃(x+y)+log₁/₃(x-y)=-1 log₁/₃(x²-y²)=log₁/₃3 x²-y²=3 ⇒
x+y=3 y=3-x
x²-y²=3 x²-(3-x)²=3 x²-9+6x-x²=3 6x=12 x=2 ⇒ y=3-2=1.
Ответ: x=2 y=1.