23.
{x;y}d.p.{2;9}
=>x/2=y/9=k
x=2k; y=9k
inlocuim x si y in fractia data:
(2•2k+6•9k)/(25•2k-9k)=58/41
(4k+54k)/(50k-9k)=58/41
58k/41k=58/41; simplificam cu k
=> 58/41=58/41, este adevarat
=>(2x+6y)/(25x-y)=58/41 este adevarata daca {x; y}d.p.{2; 9}
24.
{a;b;c;d}d.p.{5; 4; 2; 3} si bc=4d
a/5=b/4=c/2=d/3=k
=> a=5k; b=4k; c=2k; d=3k
b•c=4k•2k=8k²
8k²=4•3k /:4k
2k=3; => k=3/2
a=5•3/2=15/2
b=4•3/2=6
c=2•3/2=3
d=3•3/2=9/2
a+b+c+d=15/2 +6+3 +9/2=(15+9)/2+9=12+9=21
D21={-21; -7; -3; -1; 1; 3; 7; 21}; multimea divizorilor intregi
D21={1; 3; 7; 21}; multimea divizorilor naturali
