Question

42. Determinaţi numerele x,y,z ştiind că x+y, y+z, z+x sunt direct proporţionale cu numerele 6, 9, 13 iar xy+3xz-2yz=436

Answer 1

(x+y)/6=(y+z)/9=(z+x)/13=k
x+y=6k
y+z=9k
z+x=13k
2x+2y+2z=28k
x+y+z=14k
z=8k
x=5k
y=k
5k*k+3*5k*8k-2*8k*k=436
5k²+120k²-16k²=436
109k²=436
k²=4⇒k=2
x=10
y=2
z=16
Vf. 2*10+3*160-2*32=436