Question

If x upon 3x-y-z = y upon 3y-z-x = z upon 3z-x-y
and x+y+z is not equal to 0 then show that the values of each ratio is equal to 1
plz urgent

Answer 1

Answer:

Please see the attachment

Answer 2

x/(3x - y - z)   = y/(3y - z - x)  = z/(3z - x - y)  = 1

Step-by-step explanation:

x/(3x - y - z)   = y/(3y - z - x)  = z/(3z - x - y)  = K

=> x = 3xK - ky - kz

=> x = 3xK - ky - kz + kx - kx

=> x(1 - 4k) = -k(x + y + z)

=> k(x + y + z) = x(4 k - 1)

simialrly

   k(x + y + z) = y(4 k - 1)

   k(x + y + z) = z(4 k - 1)

=>  x(4 k - 1) = y(4 k - 1) = z(4 k - 1)

=> x = y  = z

=> k(x + x + x ) = x(4k - 1)

=> 3kx = 4kx - x

=> kx = x

=> k = 1

x/(3x - y - z)   = y/(3y - z - x)  = z/(3z - x - y)  = 1

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