Question

Det nr a,b,c,e i.p cu nr 3 ,5,9,15 stiind ca 2a-3b+c-d=15

Answer 1

a/1/3 = 3 a 
b/ 1/5 = 5 b
c/1/9 = 9 c 
d/1/15 = 15 d 

3 a = 5 b = 9 c = 15 d = k ⇒  a = k/3;  b = k/5;  c = k/9;  d = k/15 

2 k/3 - 3 k/5 + k/9 - k/15 = 15 

cmmmc al numitorilor ( 3, 5, 9, 15 ) = 3²×5= 45 
→ aducem fractiile la acelasi numitor comun 45 

2 k ×15 - 3 k × 9 + k ×5 - k ×3 = 45 ×15 

30 k - 27 k + 5 k - 3 k = 675 

5 k = 675 ⇒ k = 675 : 5 ⇒ k = 135

a = 135/3 = 45

b = 135/5 = 27

c = 135/9 = 15

d = 135/15 = 9

Verific:  2×45 - 3 × 27 + 15 - 9 = 90 - 81 + 15 - 9 = 9 + 15 - 9 = 15