Question

Numerele x,y,z sunt invers proportionale cu 1 supra 2, 1 supra 3 si 1 supra 4. Determinat x,y,z daca x*y*z=648

Answer 1

x*1/2 = y*1/3 = z*1/4 ⇔ x/2=y/3=z/4 ⇒
z=2x si y=3x/2
xyz=x*3x/2*2x = 3x^3 = 648 I :3
x^3 = 216 = 2^3 * 3^3 = (6)^3 ⇒
x=6
y=3*6/2=3*3=9
z=2*6=12