Question

nr m,n,p sunt invers proportionale cu 8,9 12. Aflati cele trei numere daca:
a)suma lor este 46
b)produsul lor este 2
PLS

Answer 1

8a = 9b = 12c = k

a = k/8

b = k/9

c = k/12

a) a+b+c = 46 =>  k/8 + k/9 + k/12 = 46 => 9k/72 + 8k/72 + 6k/72 = 46

(9k + 8k + 6k)/72 = 46 => 23k = 46x72 => k = 46x72/23 = 2x72 = 144

Atunci a = k/8 = 144/8 = 18; b = k/9 = 144/9 = 16; c = k/12 = 144/12 = 12

b) abc = 2 => k/8 x k/9 x k/12 = 2 => k^3/8x9x12 = 2 => k^3 = 2x8x9x12 = 2^6 x  3^3 => k = 2^2x3 => k = 12

Atunci a = k/8 = 12/8 = 3/2; b = k/9 = 12/9 = 4/3; c = k/12 = 12/12 = 1