if `x gt m,y gt n,z gt r (x,y,zgt 0)` such that `|{:(x,,n,,r),(m,,y,,r),(m,,n,,z):}|=0` the value of `(m)/(x-m)+(n)/(y-n) +(r )/(z-r)`isA. -2B. -4C. 0D. -1

if `x gt m,y gt n,z gt r (x,y,zgt 0)` such that `|{:(x,,n,,r),(m,,y,,r

1.	if `x gt m,y gt n,z gt r (x,y,zgt 0)` such that `\|{:(x,,n,,r),(m,,y,,r),(m,,n,,z):}\|=0` the value of `(m)/(x-m)+(n)/(y-n) +(r )/(z-r)`isA. -2B. -4C. 0D. -1
Answer» Correct Answer - D `\|{:(x,,n,,r),(m,,y,,r),(m,,n,,z):}\|=0` Applying `R_(1) to R_(1)-R_(2) " and " R_(2) to R_(2)-R_(3)` we get `\|{:(x-m,,n-y,,0),(0,,y-n,,r-z),(m,,n,,z):}\| =0` `rArr (x-m)(y-n)(n-y)(r-z)m-n(r-z)(x-m) =0` Dividing by `(x-m)(y-n)(z-r)` we have `(z)/(z-r)+(m)/(x-m) +(n)/(y-n) =0` `" or " (z)/(z-r) +(m)/(x-m) +1 +(m)/(y-n) +1=2` ` " or " (z)/(z-r) +(x)/(x-m) +(y)/(y-n) =2` `" or " (m)/(x-m)+(n)/(y-n)+(r)/(z-r)=-1` Now `,A.M ge G.M.` `rArr ((z)/(z-r)+(x)/(x-m)+(y)/(y-n))/(3)ge ((z)/((z-r))(x)/((x-m))(y)/((y-n)))^(1//3)` `" or " (z)/(z-r)(x)/(x-m) (y)/(y-n) le (8)/(27)`