Răspuns:
Explicație pas cu pas:
a) Arati ca 2020•5=2022
x = 2020
y = 5
x*y = x + y/5 + 1 = 2020 + 5/5 + 1 = 2020 + 1 + 1 = 2022
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c) Determinati numar real x pentru care 5^x * 5^(x+1) =11
x = 5^x
y = 5^(x+1)
x*y= x+ y/5 +1
5^x + 5^(x+1) / 5 + 1 = 11
5^x + 5^x = 11 -1 = 10
2*5^x = 10
5^x = 10 : 2 = 5 = 5^1
x = 1
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b) Determinati numarul real x pentru care (x*y) *x =24/5
x*y= x+ y/5 +1
(x+ y/5 +1)*x = x + y/5 + 1 + x/5 + 1 = 24/5
6x/5 + y/5 = 24/5 - 2 = 24/5 - 10/5 = 14/5
6x + y = 14
x = 1; y = 8
1*8 = 1 + 8/5 + 1 = 10/5 + 8/5 = 18/5
18/5*1 = 18/5 + 1/5 + 1 = 19/5 + 5/5 = 24/5
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