Решите систему: log₅x+log₅y=1 2 в степени (х+у-3) = 8. Created by elizavetadonch. matematika-ru

Решите систему: log₅x+log₅y=1 2 в степени (х+у-3) = 8...

July 2022 1 8 Report

Решите систему:

log₅x+log₅y=1
2 в степени (х+у-3) = 8

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Lesben Log5 x + log5 y =1 , x bolše čem 0, y bolše čem 0
2ˇ(x+y-3)=8
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log5 (xy)=1
2ˇ(x+y-3)=2³
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xy=5ˇ1
x+y-3=2
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xy=5
x+y=5
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y=5-x
x(5-x)=5
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y=5-x
5x-x²=5
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y=5-x
x²-5x+5=0, D=25-20=5 , √D=√5)
a)x1=(5+√5)/2 , y1=5-(5+√5)/2=5-2,5-√5/2=2,5-√5/2
b)x2=(5-√5)/2 , y2=5-(5-√5)/2=5-2,5+√5/2=2,5+√5/2

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