Saved Bookmarks
| 1. |
If the lines `lx+y+1=0,x+"my"+1=0" and "x+y+n=0` intersect at one point then the value of `(1)/(1-l)+(1)/(1-m)+(1)/(1-n)` is (l,m, n are unequal). |
|
Answer» Correct Answer - A Clearly, `|{:(l,1,1),(1,m,1),(1,1,n):}|=0,{:(C_(2)toC_(2)-C_(1)),(C_(3)toC_(3)-C_(1)):}" "|{:(l,1-l,1-l),(1,m-1," "0),(1," "0,n-1):}|=0` `impliesl(m-1)(n-1)+(l-1)(n-1)+(l-1)(m-1)=0" "("Expanding along "R_(1))` `:." ""On dividing by "(l-1)(m-1)(n-1)," we get "` So, `(1)/(1-l)+(1)/(1+m)+(1)/(1-n)=1.`Ans. |
|