Question

Aratati ca min(a,b)=[tex] \frac{1}{2}
[/tex] (a+b - modul de a-b)

Answer 1

Fie a,b numere reale. Demonstrati ca min{a,b}=(1/2)*(a+b-|a-b|).
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REZOLVARE

Daca a<=b:
min{a,b}=a si (1/2)*(a+b-|a-b|)=(1/2)*(a+b-(b-a))=(1/2)*(2a)=a=min{a,b}.

Daca a>b:
min{a,b}=b si (1/2)*(a+b-|a-b|)=(1/2)*(a+b-(a-b))=(1/2)*(2b)=b=min{a,b}.

Din cele doua cazuri discutate rezulta concluzia.