If 1/a+b =1/a + 1/b, then the value of a³-b³ is :

  1.  2
  2. 1
  3. 0
  4. 3
Anurag Mishra Professor Asked on 27th December 2015 in Maths.
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1 Answer(s)

Answer:  (3) 0 

Explanation:-
1/(a + b) = 1/a + 1/b
1/(a + b) = (a + b) /ab
by cross multiplication, 
ab = (a + b)^2
ab = a^2 + b^2 + 2 ab
a^2 + b^2 + ab = 0     ………………………… (1) 

Now, a^3 – b^3 = (a – b) (a^2+ b^2 + ab)
From equation (1) a^2 + b^2 + ab = 0  
Then,  a^3 – b^3 = (a – b) (0)
  a^3 – b^3 = = 

Then, the value of  a^3 – b^3  is 0 .

Hence, the correct answer is option (3) 0. 

Anurag Mishra Professor Answered on 27th December 2015.
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