logo

CuriousTab

CuriousTab

Discussion


Home Aptitude Simplification See What Others Are Saying!
  • 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


  • More questions

    • 1. 
      What is the probability that a non-leap year contains 52 Tuesday only?

    • Options
    • A. 1/7
    • B. 2/7
    • C. 3/7
    • D. 6/7
    • Discuss
    • 2. 
      7 1/ 2 - [ 2 1/ 4 ÷ { 1 1/ 4 - 1/2(1 1/ 2 - 1/3 - 1/6)}] is equal to?

    • Options
    • A. 2/9
    • B. 1
    • C. 41/2
    • D. 177/288
    • Discuss
    • 3. 
      The radius of a circle is increased so that its circumference increase by 5%. The area of the circle will increase by?

    • Options
    • A. 10 %
    • B. 10.25 %
    • C. 8.75 %
    • D. 10.5 %
    • Discuss
    • 4. 
      Yogesh can run 1km in 6 min 20 s and Vijay can cover the same distance in 6 min 40 s . By what distance can Yogesh beat Vijay?

    • Options
    • A. 50 m
    • B. 90 m
    • C. 45 m
    • D. 30 m
    • Discuss
    • 5. 
      There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank can be filled in 1 h, then how long will third pipe take to empty the full tank.

    • Options
    • A. 3 h
    • B. 4 h
    • C. 5 h
    • D. 6 h
    • Discuss
    • 6. 
      The value of (0.96) 3 - (0.1) 3/ [(0.96) 2 + (0.096) + 0.01] is?

    • Options
    • A. 0.86
    • B. 1.06
    • C. 0.95
    • D. 0.97
    • Discuss
    • 7. 
      A boy goes to school with a speed of 3 km/hr. and return to the village with a speed of 2 km/hr. If he takes 5 hours in all, then distance between the village and the school is?

    • Options
    • A. 6 km.
    • B. 7 km.
    • C. 8 km.
    • D. 9 km.
    • Discuss
    • 8. 
      Solve [(238 + 131) 2 + (238 - 131) 2] / (238 x 238 + 131 x 131)

    • Options
    • A. 4
    • B. 2
    • C. 8
    • D. 9
    • Discuss
    • 9. 
      A train 200 m long is running at a speed of 36 km/hr. It crosses a bridge in 30 sec. What is the length of the bridge?

    • Options
    • A. 150m
    • B. 200m
    • C. 125m
    • D. 100m
    • Discuss
    • 10. 
      A cistern can be filled by two pipes. A and B in 12 minutes and 14 minutes respectively and can be emptied by a third pipe C in 8 minutes. If all the taps be turned on at the same moment, what part of cistern will remain unfilled at the end of 7 minutes?

    • Options
    • A. 5/24
    • B. 19/24
    • C. 7/24
    • D. 17/24
    • Discuss


    Comments

    There are no comments.

Enter a new Comment