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Home Aptitude Simplification Comments

  • Question
  • If (a2 + 1/a2) = 17/4, then what is (a3 - 1/a3) equal to?


  • Options
  • A. 75/16
  • B. 63/8
  • C. 95/8
  • D. None of these

  • Correct Answer
  • 63/8 

    Explanation

    (a2 + 1/a2) = 17/4
    subtracts 2 and Add 2 from above equation, we will get
    ? a2 + 1/a2 - 2 + 2 = 17/4
    ? a2 + 1/a2 - 2a x 1/a + 2 = 17/4
    Now apply the formula, x2 + x2 - 2xy
    ? (a - 1/a)2 + 2 = 17/4
    ? (a - 1/a)2 = 17/4 - 2
    ? (a - 1/a)2 = (17 - 8)/4
    ? (a - 1/a)2 = 9/4
    ? (a - 1/a) = ?9/4
    (a -1/a) = 3/2
    After that, cubing On both sides, we get
    (a -1/a)3 = (3/2)3
    Apply the formula (x ? y)3 = x3 ? 3x2y + 3xy2 ? c3
    ? (x ? y)3 = x3 ? 3xy(x - y) ? y3
    ? a3 - 1/a3 - 3 x a x 1/a (a - 1/a) = 27/8
    ? a3 - 1/a3 = 27/8 + 3 x (3/2)
    ? a3 - 1/a3 = 27/8 + 9/2
    ? (a3 - 1/a3) = 63/8


  • Simplification problems


    Search Results


    • 1. 
      If a + 1/b = 1 and b + 1/c = 1, then c + 1/a =?

    • Options
    • A. 4
    • B. 24
    • C. 3
    • D. 1
    • Discuss
    • 2. 
      The value of (1 + 1/2) (1 + 1/3) (1 + 1/4) ..... (1 + 1/150) is?

    • Options
    • A. 65.5
    • B. 50.5
    • C. 105
    • D. 75.5
    • Discuss
    • 3. 
      If a + 1/a = ? 3, then the value of a6 - 1/a6 + 2 will be

    • Options
    • A. 3?3
    • B. 5
    • C. 1
    • D. 2
    • Discuss
    • 4. 
      (1 - 1/2) (1 - 1/3) (1 -1/4) (1 -1/5) ... (1 - 1/m) =?

    • Options
    • A. 1/m
    • B. m
    • C. m + 1
    • D. 1/(m - 1)
    • Discuss
    • 5. 
      [ (m - n) 3 + (n - r) 3 + (r - m) 3 ] / 6[(m - n) (n - r) (r - m)] =?

    • Options
    • A. 1/2
    • B. 1/3
    • C. 1/5
    • D. 1/6
    • Discuss
    • 6. 
      5/8 x 23/5 ÷ 4/9 =?

    • Options
    • A. 9/4
    • B. 8/4
    • C. 4/9
    • D. 6/15
    • Discuss
    • 7. 
      (0.49)4 x (0.343)4 ÷ (0.2401)4 x = (70 ÷ 100)? + 3 ?

    • Options
    • A. 3
    • B. 1
    • C. 4
    • D. 7
    • Discuss
    • 8. 
      (2.247)3 + (1.730)3 + (1.023)3 - 3 x 2.247 x 1.730 x 1.023 / ( (2.247)2 + (1.730)2 + (1.023)2 - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023) )

    • Options
    • A. 1.730
    • B. 4
    • C. 5
    • D. 5.247
    • Discuss
    • 9. 
      ( 8.73 x 8.73 x 8.73 + 4.27 x 4.27 x 4.27 ) / ( 8.73 x 8.73 - 8.73 x 4.27 + 4.27 x 4.27 ) is equal to?

    • Options
    • A. 11
    • B. 13
    • C. 11/7
    • D. None of these
    • Discuss
    • 10. 
      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


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