Triunghi dreptunghic
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Triunghi dreptunghic
Sa se studieze paritatea unui numar in functie de cuburile vecinilor lui .
Last edited by alex2008 on Wed Jun 17, 2009 10:17 am, edited 1 time in total.
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Dragoi
- Thales
- Posts: 126
- Joined: Thu Jan 31, 2008 5:57 pm
- Location: Bucharest
Fie \( a^2=b^2+c^2 \). Daca \( a \) este impar atunci \( b \) si \( c \) au paritati diferite, adica unul din numerele \( b \) sau \( c \) este par \( \Rightarrow \frac {a+b+c}{2} \in N \) si \( \frac {bc}{2} \in N \)
Daca \( a \) este par \( \Rightarrow \) \( b \) si \( c \) au aceeasi paritate.
1) \( b, c \) impare \( \Rightarrow b=2k+1 , c=2t+1 , a=2p \Rightarrow 4p^2=4k^2+4k+1+4t^2+4t+1 \Rightarrow 4p^2=2(2k^2+2k+2t^2+2t+1) \) imposibil
2) \( b,c \) pare \( \Rightarrow \frac {a+b+c}{2} \in N \) si \( \frac {bc}{2} \in N \).
Daca \( a \) este par \( \Rightarrow \) \( b \) si \( c \) au aceeasi paritate.
1) \( b, c \) impare \( \Rightarrow b=2k+1 , c=2t+1 , a=2p \Rightarrow 4p^2=4k^2+4k+1+4t^2+4t+1 \Rightarrow 4p^2=2(2k^2+2k+2t^2+2t+1) \) imposibil
2) \( b,c \) pare \( \Rightarrow \frac {a+b+c}{2} \in N \) si \( \frac {bc}{2} \in N \).
Politehnica University of Bucharest
The Faculty of Automatic Control and Computers
The Faculty of Automatic Control and Computers