Explicație pas cu pas:
(x+y)/13=(y+z)/10=(z+x)/7
x+y+z=30=>
x+y=30-z
y+z=30-x
z+x=30-y
(30-z)/13=(30-x)/10=(30-y)/7
(30-z)/13=(30-x)/10=>
13(30-x)=10(30-z)=>
390-13x=300-10z=>
90=13x-10z
(30-x)/10=(30-y)/7 =>
10(30-y)=7(30-x)=>
300-10y=210-7x =>
10y-7x=90
=> 13x-10z=10y-7x
=> 13x+7x=10y+10z
=>20x=10(y+z)
=>2x=10(30-x)
=>2x=30-x
=>3x=30
=>x=10
x=10=>10y-70=90=>10y=160=>y=16
x=10=>130-10z=90=>10z=40=>z=4
(x,y,z)€{(10,16,4)}
S€{(10,16,4)}
