Răspuns:
(x+y)(y+z)(x+z)/(xyz)=8
Explicație pas cu pas:
x, y, z lungimile laturilor unui triunghi
(y+z-x)/x=(x+z-y)/y=(x+y-z)/z
(y+z)/x-x/x=(x+z)/y-y/y=(x+y)/z-z/z
(y+z)/x -1=(x+z)/y -1=(x+y)/z -1
(y+z)/x=(x+z)/y=(x+y)/z
=> (y+z)/x=(x+z)/y=(x+y)/z=(y+z+x+z+x+y)/(x+y+z)
(y+z)/x=(x+z)/y=(x+y)/z=2(x+y+z)/(x+y+z)
(y+z)/x=(x+z)/y=(x+y)/z=2
y+z=2x
x+z=2y
x+y=2z
(x+y)(y+z)(x+z)/(xyz)=2x*2y*2z/(xyz)=2*2*2=8
