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  • Question
  • If x + 1/x = 3, then x5 + 1/x5 is equal to?


  • Options
  • A. 123
  • B. 83
  • C. 92
  • D. 112

  • Correct Answer
  • 123 

    Explanation

    x + 1/x = 3 ........................ (i)
    On squaring both side, we will get
    (x + 1/x)2 = (3)2
    Use the Square algebra formula (a + b)2 = a2 + 2ab + b2
    ? x2 + 1/x2 + 2 = 9
    ? x2 + 1/x2 = 7 ..................(ii)
    Again squaring both sides, we will get
    (x2 + 1/x2)2 = (7)2
    Use the Square algebra formula (a + b)2 = a2 + 2ab + b2
    ? x4 + 1/4 + 2 = 49
    ? x4 + 1/x4 = 47 .....................(iii)
    On cubing the equation (i) both side, we will get
    (x + 1/x)3 = (3)3
    Use the cube algebra formula (a + b)3 = a3 + 3a2b + 3ab2 + b3
    ? x3+ 1/x3 + 3(x + 1/x) = 27
    ? x3 + 1/x3 + 9 = 27 [? (x + 1/x) = 3]
    ? x3 + 1/x3 = 18 ...................(iv)
    On multiplying Eqs. (i) and (iii) , we get
    ? (x4 + 1/x4) (x + 1/x) = 47 x 3
    ? x5 + 1/x5 + x3 + 1/x3 = 141
    ? x5 + 1/x5 + 18 = 141 [from Eq. (iv)]
    ? x5 + 1/x5 = 123


  • More questions

    • 1. 
      The value of 47 / 10000 is?

    • Options
    • A. .0047
    • B. .0470
    • C. .00047
    • D. .000047
    • Discuss
    • 2. If 4x = 18y, then the value of ( x/y - 1) is

    • Options
    • A. 1 3
    • B. 7 2
    • C. 2 3
    • D. 3 2
    • Discuss
    • 3. 
      If the price of 23 toys is Rs. 276, then what will the price (Rs.) of 12 toys?

    • Options
    • A. 144
    • B. 158
    • C. 159
    • D. 166
    • Discuss
    • 4. 
      .02 =(......?.....)%

    • Options
    • A. 20
    • B. 2
    • C. .02
    • D. .2
    • Discuss
    • 5. 
      If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?

    • Options
    • A. 45
    • B. 55
    • C. 60
    • D. 72
    • Discuss
    • 6. 
      2?63 / 11 =233

    • Options
    • A. 4
    • B. 3
    • C. 6
    • D. 5
    • Discuss
    • 7. 
      When 121012 is divided by 12, the remainder is

    • Options
    • A. 0
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 8. 
      Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

    • Options
    • A. 18 days
    • B. 21 days
    • C. 3 days
    • D. 6 days
    • Discuss
    • 9. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 10. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss


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