Home
Class 11
MATHS
If the points ((a^3)/((a-1))),(((a^2-3))...

If the points `((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),((b^2-3)/((b-1)))`,`((c^3)/(c-1))` and `(((c^2-3))/((c-1))),` where `a , b , c` are different from 1, lie on the `l x+m y+n=0` , then (a) `a+b+c=-m/l` (b)`a b+b c+c a=n/l` (c)`a b c=((m+n))/l` (d)`a b c-(b c+c a+a b)+3(a+b+c)=0`

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that |(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2))|=(a-b)(b-c)(c-a)

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

If l n(a+c),l n(a-c)a n dl n(a-2b+c) are in A.P., then (a) a ,b ,c are in A.P. (b) a^2,b^2, c^2, are in A.P. (c) a ,b ,c are in G.P. d. (d) a ,b ,c are in H.P.

If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coefficients, then n= (a c+a b+b c)/(b^2+a c) b. (2a c+a b+b c)/(b^2-a c) c. (a b+a c)/(b^2-a c) d. none of these

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

Prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

Given |(a,a^(2),a^(3)+1),(b,b^(2).b^(3)+1),(c,c^(2)+c^(3)+1)|=0 and a ne b ne c .Show that abc=-1

(a) If x + y + z=0, show that x ^(3) + y ^(3) + z ^(3)= 3 xyz. (b) Show that (a-b) ^(3) + (b-c) ^(3) + (c-a)^(3) =3 (a-b) (b-c) (c-a)

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then (a) a+b+c=0 (b) a+b=2 (c) b-c=1 (d) a+c=-2

If 1/(b-a)+1/(b-c)=1/a+1/c , then A. a ,b ,a n dc are in H.P. B. a ,b ,a n dc are in A.P. C. b=a+c D. 3a=b+c