система логарифмических неравенств 11 класс
помогите решить
{
[tex] log_{5}(x + y) = 1[/tex]
[tex] log_{2}(y) + log_{2}(x) = 1 + log_{2}(3) [/tex]
}
помогите решить
{
[tex] log_{5}(x + y) = 1[/tex]
[tex] log_{2}(y) + log_{2}(x) = 1 + log_{2}(3) [/tex]
}
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Verified answer
Log₅(x+y)=1 x+y=5¹ x+y=5 y=5-xlog₂y+log₂x=1+log₂3 log₂xy/3=1 xy/3=2¹ x(5-x)=6 5x-x²=6 x²-5x+6=0
x²-5x+6=0 D=1
x₁=3 y₁=2
x₂=2 y₂=3.