Let x = (√13+√11)/(√13 – √11 and y=1, then the Value of 3x²-5xy+3y² is :

  1. 1171
  2. 1177
  3. 1771
  4. 1717
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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  • 1 Answer(s)

    Answer is (4): 1717

    Explanation:-

    x = (√13+√11)/(√13 – √11)
    = (√13 + √11) (√13 + √11)/(√13 – √11) (√13 + √11)
    = (√13 + √11)²/(√13)² – (√11)²
    = {(√13)² + (√11)² + 2√13 x √11}/13 – 11
    = (13 + 11 + 2 √13 √11)/2
    = (24 + 2 √13 √11)/2
    = 2 (12 + √13 √11)/2
    x = 12 + √13 √11 and y = 1

    Then, the value of 3x² -5 xy + 3 y²
    Put the value of x = 12 + √13 √11 and y = 1
    Then, 3 ( 12 + √13 √11)² – 5  (12 + √13 √11) (1) + 3 (1)²
    = 3 (12)² + (√13 √11)² + 2 x 12 x √13 √11 – 60 + 5√13 √11 + 3
    = 3 x 144 + 13 x 11 + 24√13 √11 – 60 + 5√13 √11 + 3
    = 432 + 143 – 60 +3 + 24√13 √11 + 5√13 √11
    = 518 + 29√13 √11
    = 518 + 29 x 3.6 x 3.31
    = 518 +

    Monis Rasool Professor Answered on 28th October 2015.
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