Question

Aflati numerele x,y si z stiind ca sunt direct proportionale cu 3,7 si 2 iar xy+yz=175

Raspunsul postat:
X / 3=y /7=z / 2= K x /3=k=x=3k y /7=k=y=7k z /2=k=z=2k 3k*7k +7k*2k=175 21k+14k=175 35k=175 k=175 : 35 k=5 x=3*5 x=15 y=7*5 y=35 z=2*5 z=10

Nu cred ca e corect, pentru ca 3k*7k+7k*2k=21k*k+14k*k=35k*k=175 => k*k=5
Am dreptate?

Answer 1

X / 3=y /7=z / 2= K x /3=k=x=3k y /7=k=y=7k z /2=k=z=2k 3k*7k +7k*2k=175 21k+14k=175 35k=175 k=175 : 35 k=5 x=3*5 x=15 y=7*5 y=35 z=2*5 z=10 SPER SA TE AJUTE

Answer 2

{x ,y ,z} d.p. {3 , 7, 2}

x/3=k⇒ k=3k
y/7=k⇒y=7k
z/2=k⇒z=2k
xy+yz=175⇒y(x+z)=175

7k×(3k+2k)=175⇒7k × 5k=175⇒35k²=175

k=√5

x=3k=3√5

y=7k=7√5

z=2k=2√5

verificare

xy+yz=y(x+z)=175

7√5(3√5+2√5)=175

7√5×5√5=175

7×5×5=175

175=175