Răspuns :
a + b = 49
a = 7x
b = 7y
7x + 7y = 49
7 (x + y) = 49
(x + y) = 49 : 7
x + y = 7
(x,y) ∈ {(1,6) ; (2,5); (3,4)}
(a,b) ∈ {(7,42); (14,35) ; (21,28)}
a+b=49
cmmdc al lui a si b=7 =>
a=7×x
b=7×y
7×x+7×y=49
7×(x+y)=49
x+y=49:7
x+y=7
cautam toate probabilitățile lui x si y pana aflăm cu cat sunt egale =>
daca x=1 => y=7-1=6
x+y=1+6=7
a=7×x=7×1=7
b=7×6=42
7+42=49 (adevarat )
___________________
daca x=2 => y=7-2=5
x+y=2+5=7
a=7×x=7×2=14
b=7×y=7×5=35
a+b=14+35=49 (adevărat)
_____________________
daca x=3 => y=7-3=4
x+y=3+4=7
a=7×x=7×3=21
b=7×y=7×4=28
a+b=21+28=49 (adevărat )
__________________
daca x=4 => y=7-4=3
x+y=4+3=7
a=7×x=7×4=28
b=7×y=7×3=21
a+b=28+21=49 (adevărat )
_____________________
daca x=5 => y=7-5=2
x+y=5+2=7
a=7×x=7×5=35
b=7×y=7×2=14
a+b=35+14=49 (adevărat )
__________________
daca x=6 => y=7-6=1
x+y=7
a=7×x=7×6=42
b=7×y=7×1=7
a+b=42+7=49 (adevarat )
a={7, 14, 21,28, 35,42}
b={ 42,35,28,21,14,7 }
cmmdc al lui a si b=7 =>
a=7×x
b=7×y
7×x+7×y=49
7×(x+y)=49
x+y=49:7
x+y=7
cautam toate probabilitățile lui x si y pana aflăm cu cat sunt egale =>
daca x=1 => y=7-1=6
x+y=1+6=7
a=7×x=7×1=7
b=7×6=42
7+42=49 (adevarat )
___________________
daca x=2 => y=7-2=5
x+y=2+5=7
a=7×x=7×2=14
b=7×y=7×5=35
a+b=14+35=49 (adevărat)
_____________________
daca x=3 => y=7-3=4
x+y=3+4=7
a=7×x=7×3=21
b=7×y=7×4=28
a+b=21+28=49 (adevărat )
__________________
daca x=4 => y=7-4=3
x+y=4+3=7
a=7×x=7×4=28
b=7×y=7×3=21
a+b=28+21=49 (adevărat )
_____________________
daca x=5 => y=7-5=2
x+y=5+2=7
a=7×x=7×5=35
b=7×y=7×2=14
a+b=35+14=49 (adevărat )
__________________
daca x=6 => y=7-6=1
x+y=7
a=7×x=7×6=42
b=7×y=7×1=7
a+b=42+7=49 (adevarat )
a={7, 14, 21,28, 35,42}
b={ 42,35,28,21,14,7 }