If the lines `a x+y+1=0,x+b y+1=0a n dx+y+c=0(a ,b ,c` being distinct and different from `1)` are concurrent, then prove that `1/(1-a)+1/(1-b)+1/(1-c)=1.`

If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct and different from 1) are concurrent the value of (a)/(a-1)+(b)/(b-1)+(c)/(c-1) is

If (a, 1, 1), (1, b, 1) and (1, 1, c) are coplanar then prove that (1)/(1-a)+(1)/(1-b)+(1)/(1-c)=1 .

If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 are concurrent then prove that, (1)/( 1-a) + (1) /( 1-b) + (1) /( 1-c) = .

The lines ax + 2y + 1 = 0, bx + 3y +1 =0 and cx + 4y + 1=0 are concurrent if a, b, c are in A.P.

If the points A(x,y), B(a,0) and C(0,b) are collinear, prove that (x)/(a) + (y)/(b) = 1

If three lines whose equations are y=m_(1) x+c_(1), y=m_(2) x + c_(2) and y=m_(3) x + c_(3) are concurrent, then show that m_(1) (c_(2) - c_(3))+m_(2) (c_(3) - c_(1) ) + m_(3) ( c_(1) - c_(2) ) =0 .

If y= sin^(-1)x then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x (dy)/(dx)=0

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

If a^(x)=b, b^(y)=c,c^(z)=a, prove that xyz = 1 where a,b,c are distinct numbers

If a, b, x, y are positive natural numbers such that (1)/(x) + (1)/(y) = 1 then prove that (a^(x))/(x) + (b^(y))/(y) ge ab .