Question

Numerele x si 2 sunt direct proportionate cu y si 3 iar y si 3 sunt direct proportionate cu z si 5.  Aflati x y z, stiind ca x la puterea a 2 + y la puterea a 2 = 117

Answer 1

x/y=2/3 ⇒ x/2=y/3; y/z=3/5 ⇒ y/3=z/5 ⇒ x/2=y/3=z/5=k ⇒ x=2k, y=3k, z=5k;
x²+y²=117 ⇒ 4k²+9k²=117 ⇒ k²=9, k=3 ⇒ x=6, y=9, z=15.