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If x/y+z=y/z+x=z/x+y=k then show that k=1/2 if x, y, z are not equal to 0

If x/y+z=y/z+x=z/x+y=k then show that k=1/2 if x, y, z are not equal to 0

Grade:12th pass

2 Answers

Shashank Singh
askIITians Faculty 57 Points
6 years ago
1+ x/(y+z)= k+1
1+y/(x+z)= k+1
1+ z/(x+y)= k+1
(y+z)/(x+y+z)=1/(k+1)
(x+z)/(x+y+z)=1/(k+1)
(x+y)/(x+y+z)= 1/(k+1)
on adding above three equations
2(x+y+z)/(x+y+z)=3/(k+1)
k+1=3/2
k=1/2 [ans]
Yoshita Shah
13 Points
4 years ago
x=k(y+z)
y=k(z+x)
z=k(x+y)
 
x+y+z= [k(y+z) + k(z+x) + k(x+y)]
x+y+z= k [ y+z+z+x+x+y]
x+y+z= k [ 2x+2y+2z]
x+y+z= 2k[ x+y+z]
x+y+z/x+y+z=2k
1=2k
k=1/2

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