Find The Value ? If

1/(√7 – √6) – 1/ (√6 – √5) + 1/ (√5 – 2) – 1 /(√8 – √7) + 1/ (3 – √8)

  1. 5
  2. 0
  3. 1
  4. 7
Anurag Mishra Professor Asked on 12th August 2015 in Maths.
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  • 1 Answer(s)
    Best answer

    Answer: (1) 5

    Explanation:-
    1/(√7 – √6) – 1/ (√6 – √5) + 1/ (√5 – 2) – 1 /(√8 – √7) + 1/ (3 – √8)
    = 1 (√7 + √6)/(√7 – √6) (√7 + √6)  –  1 (√6 + √5) / (√6 – √5) (√6 + √5)  + 1 (√5 + 2) / (√5 – 2) (√ 5 + 2) – 1 (√8 + √7) / (√8 – √7) (√8 + √7)  + 1 (3 + √8 ) / (3 – √8) (3 + √8)
    =  (√7  + √6) / (7 – 6)  – (√6 + √5) / (6 – 5)  + (√5 + 2) / (5 – 4)  – (√8 – √7) / (8 – 7)  +  (3 + √8) / (9 – 8)
    = (√7 + √ 6) / 1 – (√6 + √5) / 1 + (√5 + 2) / 1  – (√8 – √7) / 1 + (3 + √8) /1
    = √7 + √6  – √6 – √5 + √5  + 2 – √8 – √7 + 3 + √8
    = 2 + 3
    = 5

    Hence, the answer is (1) 5.

    Anurag Mishra Professor Answered on 13th August 2015.
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