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exercitiu matematica

 
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Andra



Joined: 20 Oct 2013
Posts: 1

PostPosted: Sun Oct 20, 2013 12:30 pm    Post subject: exercitiu matematica Reply with quote

determinati numerele naturale a,b stiind ca indeplinesc simultan conditiile : (a,b)=15 si a +b=180
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Laurian Filip
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Joined: 25 Nov 2007
Posts: 473
Location: Bucuresti

PostPosted: Mon Oct 21, 2013 3:19 pm    Post subject: Reply with quote

(a,b)=15 => a=15p , b=15q si (p,q)=1

Inlocuind in relatia initiala avem:
15p+15q=180
15(p+q)=180
p+q=12

Deoarece (p,q)=1, ultima egalitate are ca solutii: (1,11), (5,7) , (7,5), (11,1) si deci solutiile ab sunt (15, 165), (75, 105), (105,75), (165,15)
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