Question

(A,B)=15
AxB= 1350
A=?
B=?

Answer 1

daca (a,b)=15 ⇒exista numerele naturale prime intre ele m si n astfel incat
a=15m
b=15n
inlocuim in produs
15m·15n=1350
mn=6
pentru ca m si n sa fie prime intre ele avem cazurile
1. m=1, n=6 ⇒a=15, b=90
2. m=2, n=3⇒ a=30, b=45
3. m=3, n=2 (este invers ca la 2)
4. m=6, n=1 (invers ca la 1)
solutiile sunt perechile de numere
S={(15,90), (30,45), (45,30), (90,15)}

Answer 2

∅ Rezolvare :



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→ ( a,b ) = 15 → a = 15x si b = 15y →
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→ ( x,y ) = 1
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→ a • b = 1 350 → 15x • 15y = 1 350
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x • y = 1 350 : 225 = 6 y = 6 →
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y = 1 → x = 6 → a = 15 • 6 → a = 90 → b = 15 • 1 → b = 15
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y = 2 → x = 3 → a = 15 • 3 → a = 45 → b = 15 • 2 → b = 30
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y = 3 → x = 2 → a = 15 • 2 → a = 30 → b = 15 • 3 → b = 45
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y = 6 → x = 1 → a = 15 • 1 → a = 15 → b = 15 • 6 → b = 90
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S = { ( 90 , 15 ) , ( 45 , 30 ) , ( 30 , 45 ) , ( 15 , 90 ) }

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