Question

Ma puteti ajuta ?
1. Determinati nr. naturale a si b , astfel incat
(a+2)•(b-3)=28
2. Idrntificati un factor comun, in fiecare suma, calculati:
10+20+30+....+1230=
7+14+21+....+315=
3.In cate zerouri se termina produsul pri.elor 25 de nr. naturale nenule ?

Answer 1

(a+1)*(b-3)=28

28=1*28
a+1=1  ⇒a=0
b-3=28 ⇒b=8

28=2*14
a+1=2  ⇒a=1
b-3=14 ⇒b=17

28=4*7
a+1=5  ⇒a=4
b-3=7 ⇒b=10

28=7*4
a+1=7  ⇒a=6
b-3=4 ⇒b=7

28=14*2
a+1=14  ⇒a=13
b-3=2 ⇒b=5


28=28*1
a+1=28  ⇒a=27
b-3=1 ⇒b=4


10+20+30+....+1230= 10(1+2+3...+123)=123(123+1)/2=123*62=7626
7+14+21+....+315= 7((1+2+3...+45)=45(45+1)/2=45*23=1035
 
3.In cate zerouri se termina produsul prielor 25 de nr. naturale nenule ?
1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20*21*22*23*24*25=
cautam de cate ori apare 5
5  =5    1 data
10 =2*5   1 data
15 =3*5   1 data
20=4*5  1 data
25=5*5  de 2 ori
1+1+1+1+2=6 zerouri