Question

x/(q-r) = y/(r-p) = z/(p-q), show p+q+r=0​

Answer 1

x/(q-r) = y/(r-p) = z/(p-q)  shown  x+y+z=0​  

Step-by-step explanation:

x/(q-r) = y/(r-p) = z/(p-q), show p+q+r=0​

Question is either incomplete or incorrect

as For example  

x = 1    y =-2      z = 1

p  = 1   q = 2  r = 3

satisfies x/(q-r) = y/(r-p) = z/(p-q) = - 1  this

but p + q + r  = 6 ≠ 0

but x + y + z = 0

i think Correct Question should be

x/(q-r) = y/(r-p) = z/(p-q), show x+y+z=0​  

let say

x/(q-r) = y/(r-p) = z/(p-q) = k

=> x = kq - kr

    y = kr - kp

   z = kp - kq

Adding all

x + y + z =  kq - kr + kr - kp +  kp - kq

=> x + y + z = 0

Learn more:

28. If x = a(bc), y = b(c - a), z = c(a - b)

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