The value of {3√7/ (√5+√2)] – [ 5√5/(√2+√7)] + [2√2/ (√7+√5)] is :

  1. 1
  2. 0
  3. 2√3
  4. √7
Anurag Mishra Professor Asked on 27th December 2015 in Maths.
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  • 1 Answer(s)

    Answer:  (2) 0 

    Explanation:-
    [3√7/ (√5+√2)] – [ 5√5/(√2+√7)] + [2√2/ (√7+√5)]
    = [3√7(√5 – √2)/(√5 + √2) (√5 – √2)] – [5√5 (√7 – √2)/(√7 + √2) (√7 – √2)] + [2√2 (√7 – √5)/(√7 + √5) (√7 – √5)]
    = [3√7(√5 – √2)/(5 – 2)] – [5√5 (√7 – √2)/(7 – 2)] +  [2√2 (√7 -√5)/(7 – 5)]
    = [3√7(√5 – √2)/3] – [5√5 (√7 – √2)/5] + [2√2 (√7 -√5)/2]
    = [10 x 3√7(√5 – √2) – 6 x 5√5 (√7 – √2) + 15 x 2√2 (√7 – √5)]/30
    = (30√7√5 – 30√7√2 – 30√5√7 + 30√5√2 + 30√2√7 – 30√2√5)/30
    = (30√7√5 – 30√5√7 + 30√2√7 – 30√7√2 + 30√5√2- 30√2√5)/30
    = 0/30
    = 0

    Then, the value of [3√7/ (√5+√2)] – [ 5√5/(√2+√7)] + [2√2/ (√7+√5)] is 0.

    Hence, the correct answer is option (2) 0.

    Anurag Mishra Professor Answered on 28th December 2015.
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