1/sqrt.3 + 1/(3 + sqrt.3) + 1/(sqrt.3 – 3) is

The value of
(a) 3
(b) sqrt.3
(c) 0
(d) None of these

Anurag Mishra Professor Asked on 31st March 2016 in Maths.
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1 Answer(s)

Answer: (c) 0 

Solution:-
1/√3 + 1/(3 + √3) + 1/(√3 – 3)
√3/√3√3 + (3 – √3)/(3 + √3) (3 – √3) + (√3 + 3)/(√3 – 3) (√3 + 3)
√3/3 + (3 – √3)/(9 – 3) + (√3 + 3)/(3 – 9)
√3/3 + (3 – √3)/6 + (√3 + 3)/(-6)
√3/3 + (3 – √3)/6 – (√3 + 3)/(6)
√3/3 + (3 – √3 – √3 – 3)/6
√3/3 – 2√3/6
= √3/3 – √3/3
= 0

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

Anurag Mishra Professor Answered on 2nd April 2016.
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