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  • Question
  • If x = ( ? 3 + 1 ) / ( ? 3 - 1 ) and y = ( ? 3 - 1) / ( ? 3 + 1 ) , then the value of x2/y + y2/x is?


  • Options
  • A. 52
  • B. 76
  • C. 4
  • D. 64

  • Correct Answer
  • 52 

    Explanation

    Given, x = ( ?3 + 1) / ( ?3 - 1 )
    y = ( ?3 - 1 ) / ( ?3 + 1 )
    Then , x + y = { ( ?3 + 1) / ( ?3 - 1 ) } + { ( ?3 - 1 ) / ( ?3 + 1 ) }
    ? x + y = { (?3 + 1)2 + (?3 - 1)2 } / (?3 - 1) (?3 + 1)
    ? x + y = ( 3 + 1 +2?3 + 3 + 1 - 2?3 ) / ( 3 - 1 )
    ? x + y = 8/2
    ? x + y = 4 --------------------(1)
    Now xy = ( ?3 - 1 / ?3 + 1 ) x ( ?3 + 1 / ?3 - 1 )
    xy = (3 - 1) / (3 - 1) = 2/2 = 1------------------(2)
    Given in question,
    ? x2/y + y2/x
    = ( x3 + y3 )/xy
    ------------------- (3)
    Apply the algebra formula, A3 + B3 = (A + B)3 - 3AB(A + B)
    = (x + y)3 - 3xy(x + y)/xy
    Put the value of x + y from (1) and xy from (2) in Equation (3), we will get
    = (4)3 - 3 x 1 x (4)/1
    = 64 - 3 x 1 x 4
    = 64 - 12
    = 52


  • Simplification problems


    Search Results


    • 1. 
      If a = ( ?2 -1)1/3, then the value of (a - a-1)3 + 3 ( a - a -1 ) is?

    • Options
    • A. -2
    • B. 2
    • C. 2?2
    • D. ?2
    • Discuss
    • 2. 
      If ?28 - 6?3 = ?3a + b, (where a, b are rationals), value of (a + b) is?

    • Options
    • A. -2
    • B. 2
    • C. 1
    • D. -1
    • Discuss
    • 3. 
      If x + a/x = 1, then the value of ( x2 + x + a ) / (x3 - x2) is?

    • Options
    • A. -2
    • B. -a/2
    • C. 2/a
    • D. -2/a
    • Discuss
    • 4. 
      1/(1 x 4) + 1/(4 x 7) + 1/(7 x 10) + 1/(10 x 13) + 1/(13 x 16) =?

    • Options
    • A. 5/16
    • B. 3/16
    • C. 7/16
    • D. 11/16
    • Discuss
    • 5. 
      If x = ( ?2 + 1 ) / ( ?2 - 1 ) and x - y = 4?2, then the value of (x2 + y2) is?

    • Options
    • A. 34
    • B. 38
    • C. 30
    • D. 32
    • Discuss
    • 6. 
      If x + a/x = b , then the value of ( x2 + bx + a) / ( bx2 - x3 ) is?

    • Options
    • A. a + b
    • B. 2b/a
    • C. b/a
    • D. ab
    • Discuss
    • 7. 
      51.3 + 7.078 +1.38 + 0.9 =?

    • Options
    • A. 61.668
    • B. 59.238
    • C. 60.658
    • D. None of these
    • Discuss
    • 8. 
      The product of 3.5413 x 2.1 is

    • Options
    • A. 7.44673
    • B. 7.43673
    • C. 7.53673
    • D. None of these
    • Discuss
    • 9. 
      [( 3.242 x 14 ) / 100] =?

    • Options
    • A. 0.045388
    • B. 4.5388
    • C. 453.88
    • D. None of these
    • Discuss
    • 10. 
      9.724 ÷ 100 =?

    • Options
    • A. 972.4
    • B. 9.724
    • C. 0.09724
    • D. None of these
    • Discuss


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