1)Daca a supra b =3 supra 7,calculati 3a+8b supra 8b si 5a supra 5a+6b.
2)Daca 2x supra 5y=3 supra 8 si x+y=93,afla numerele x si y.
3)Daca 2a+5b supra 3a+8b=19 supra 30 si b-a=1,afla numerele a si b.
4)Daca a supra 2=b supra 5, b supra 3=c supra 4 si a+b+c=410,afla a,b,c.
5)Afla numerele naturale a,b,c stiind ca a supra 2=3 supra b=c supra 5…Ma ajutati voi?
Crisadi1185user (0)
1)
Metoda 1
(3a+8b)/8b=(3a/8b) +1=(3/8)*(a/b) +1=(3*3+56)/8*7
Metoda 2
a / b =3/7 sau a/3=b/7=k , (3,7)=1 rezulta k E N* si a=3k , b=7k
5a/(5a+6b)=5*3k / (5*3k + 6*7k)=15k/57k=5/19
2)
2x /5y=3 / 8 rezulta 2x/3=5y/8 avem (3,8)=1 si [2,5]=10
Rezulta proportiile derivate : 2x/3=10x/15=10y/16=10*(x+y)/(15+16)=10*93/31=30 rezulta x=3*30:2= si y=
3)
(2a+5b) / (3a+8b)=19 / 30 echivalent cu (2a+5b) / 19 = (3a+8b) / 30=(2*(3a+8b) – 3*(2a+5b)) /(2*30 – 3*19) =b/3=( 8*(2a+5b) – 5*(3a+8b)) /(8*19 – 5*30)=a/2=(b-1)/(3-2)=1 rezulta a si b
4)
a/2=b/5 |:3, b/3=c/4 |:5 , [3,5]=15 rezulta a/6=b/15=c/20=(a+b+c)/(6+15+20)= continua tu
5) a/2=3/b=c/5=k ,(2,5)=1 rezulta k E N* rezulta 3/b E N* rezulta b E D3={1,3}
b=1 rezulta
b=3 rezulta
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