badge image

Enroll For Free Now & Improve Your Performance.

User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.

Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: Rs.

There are no items in this cart.
Continue Shopping


1/(w+a)+1/(w+b)+1/(w+c)=2w 2 and 1/(w 2 +a)+1/(w 2 +b)+1/(w 2 +c)=2w what is 1/(a+1)+1/(b+1)+1/(c+1)= A)2 B)-2 C)w 2 D)w where w is a complex cube root of unity.

11 years ago

Answers : (4)

Badiuddin askIITians.ismu Expert
147 Points

Dear srichaitanya

let f(z) =1/(z+a)+1/(z+b)+1/(z+c)  a function in z

    given f(w) =2w2

and        f(w2)=2w

clearly one of the possible function is



so f(1)=2

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE preparation.

 All the best
Askiitians Experts

11 years ago
mycroft holmes
272 Points

I wonder what is the basis for assuming that f(z) = z2 here.


Multiplying the first relation by w, we get


w/w+a + w/w+b + w/w+c = 2


or a/w+a + b/w+b + c/w+c = 1


Similarly from the second relation, we get a/a+w2 + b/b+w2 + c/c+w2 = 1


Thus, w and w2 are the roots of a/(x+a) + b/(x+b) + c/(x+c) = 1


which simplifies to x3 - (ab+bc+ca)x -2abc = 0. This means that the sum of roots of this cubic is zero. Let the third root be r.


Then r + w+w2 = 0 which means r = 1.


Thus a/a+1 + b/b+1 + c/c+1 = 1 or 1/a+1 + 1/b+1 + 1/c+1 = 2

10 years ago
Ass satwik
12 Points
Can you expalex me the step 
a/a+w + b/b+w + c/c+w = 1
2 years ago
20 Points
W3 = 1 therefore w x w​= 1 therefore w​= 1/w --(1)
1/a+w + 1/b+w +  1/c+w = 2w​= 2/w. (From 1)
Now take conjugate of the above entire equation, we get (I am representing conjugate of w as “p" for convenience)
1/a+p + 1/b+p + 1/c+p = 2/p
Now w is -1/2 +root3/2 and w²  is -1/2 – root 3/2 which is just the same as conjugate of w
Therefore w² =p
1/ a+w2 + 1/b+w2 + 1/c+w2 = 2/w2
So w and w2 are riits of equation 1/a+x + 1/b+x + 1/c+x = 2/x
Nowhow puthow x=1 to get the answer as 2.
one year ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution

Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details