Система 5^x - 5^y=100 5^(x-1) + 5^(y-1) =30

Question

Система 5^x - 5^y=100 5^(x-1) + 5^(y-1) =30

Answer 1

5^x - 5^y=100

5^(x-1) + 5^(y-1) =30

 

Пусть 5^x=a, 5^y=b

 

a-b=100

a/5+b/5=30

 

a-b=100
(a+b)/5=30

 

a-b=100
a+b=150

 

a=b+100

b=25

 

a=125⇒x=3

b=25⇒y=2

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