Question

Aflati x , y, z ∈ Q*+ , stiind ca x si y sunt direct proportionale cu 2 si 3, y si z sunt direct proportionale cu 5 si 4 si x²+y²+z²=469/16

Answer 1

x/2=y/3 ⇒ x/10=y/15; y/5=z/4 ⇒ y/15=z/12; din cele doua rezulta x/10=y/15=z/12=k,
x=10k, y=15k, z=12k ⇒ 100k²+225k²+144k²=469/16 ⇒ 469k²=469/16 ⇒ k=1/4 ⇒
x=5/2, y=15/4, z=3.