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  • Question
  • 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

  • Correct Answer


  • Explanation

    Given equation is,
    a + 1/a = ?3 .............................(i)
    On squaring both sides
    ? a2 + 1/a2 + 2 = 3
    ? a2 + 1/a2 = 1 ..............................(ii)

    Now, multiplying Equation (i) and (ii), we get
    (a + 1/a) (a2 + 1/a2) = ?3
    ? a3 + a/a2 + a2/a + 1/a3 = ?3
    ? a3 + 1/a3 + ( a + 1/a ) = ?3
    now put the value of a + 1/a in above equation,
    ? a3 + 1/a3 + ?3 = ?3 [from Eq. (i)]
    ? a3 + 1/a3 = 0
    ? ( a6 + 1 ) /a3 = 0
    ? a6 + 1 = 0 x a3
    ? a6 + 1 = 0
    ? a6 = -1
    ? a6 - 1/a6 + 2
    put the value of a6
    = (-1)6 - 1/(-1)6 + 2
    = 1 - 1 + 2 = 2


  • Simplification problems


    Search Results


    • 1. 
      (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
    • 2. 
      [ (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
    • 3. 
      If p + q = 10 and pq = 5, then the numerical value if p/q + q/p will be?

    • Options
    • A. 22
    • B. 18
    • C. 16
    • D. 20
    • Discuss
    • 4. 
      If x + y = 1, then the value of (x3 + y3 + 3xy) is?

    • Options
    • A. -2
    • B. 1
    • C. 2
    • D. 3
    • Discuss
    • 5. 
      If x + y = 18 and xy = 72, what is the value of x2 + y2?

    • Options
    • A. 120
    • B. 90
    • C. 180
    • D. Cannot be determined
    • Discuss
    • 6. 
      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
    • 7. 
      If a + 1/b = 1 and b + 1/c = 1, then c + 1/a =?

    • Options
    • A. 4
    • B. 24
    • C. 3
    • D. 1
    • Discuss
    • 8. 
      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
    • Discuss
    • 9. 
      5/8 x 23/5 ÷ 4/9 =?

    • Options
    • A. 9/4
    • B. 8/4
    • C. 4/9
    • D. 6/15
    • Discuss
    • 10. 
      (0.49)4 x (0.343)4 ÷ (0.2401)4 x = (70 ÷ 100)? + 3 ?

    • Options
    • A. 3
    • B. 1
    • C. 4
    • D. 7
    • Discuss


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