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  • Question
  • 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

  • Correct Answer
  • 34 

    Explanation

    Given that,
    x = ( ?2 + 1 ) / ( ?2 - 1 )
    Expanding given equation by multiplying and dividing with ?2 + 1
    we will get,
    ? x = ( ( ?2 + 1 ) / ( ?2 - 1 ) ) x ( ( ?2 + 1 ) / ( ?2 + 1 ) )
    ? x = ( ?2 + 1 ) x ( ?2 + 1 ) / ( ?2 - 1 ) x ( ?2 + 1 )
    ? x = ( ?2 + 1 ) 2 / ( ?2 - 1 ) x ( ?2 + 1 ) [ Use the formula (A + B)(A - B) = A2 - B2 ]
    ? x = ( ?2 + 1 ) 2 / ( ?22 - 12 ) [ Use the formula (A + B)2 = A2 + 2AB + B2 ]
    ? x = ( 2 + 1 + 2?2 ) / (2 - 1)
    ? x = 3 + 2?2 .....................(i)
    and given in question x - y = 4 ?2
    ? y = x - 4?2
    Put the value of x [ from Equation (i) ]
    ? y = 3 + 2?2 - 4?2
    ? y = 3 - 2?2
    Now, x2 + y2 = (3 + 2?2)2 + (3 - 2?2)
    Use the Algebra formula and solve the equation.
    [ Use the formula (A + B)2 = A2 + 2AB + B2 ]
    [ Use the formula (A - B)2 = A2 - 2AB + B2 ]

    ? x2 + y2 = 9 + 8 + 12?2 + 9 + 8 - 12?2
    ? x2 + y2 = 34


  • More questions

    • 1. 
      The product of two consecutive odd numbers is 19043. Which is the smaller one?

    • Options
    • A. 137
    • B. 131
    • C. 133
    • D. 129
    • Discuss
    • 2. 
      The angle of elevation of the top of a hill from each of the vertices A, B, C of a horizontal triangle is ?. The height of the hill is :

    • Options
    • A. b tan ? cosec B
    • B. a tan ? cosec A 2
    • C. c tan ? cosec C 2
    • D. None of these
    • Discuss
    • 3. 
      From a point on a circular tract 5 Km long A, B and C started running in the same direction at the same time with speeds of 2 1? 2 Km/h, 3 Km/h and 2 Km/h. respectively. Then on the starting point all three will meet again after :

    • Options
    • A. 30 hours
    • B. 6 hours
    • C. 10 hours
    • D. 15 hours
    • Discuss
    • 4. 
      The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is?

    • Options
    • A. 29.46 km/hr.
    • B. 31.68 km/hr.
    • C. 36.25 km/hr.
    • D. 32.72 km/hr.
    • Discuss
    • 5. 
      A library has two books each having three copies and three other books each having two copies. In how many ways can all these books be arranged in a shelf so that copies of the same book are not separated?

    • Options
    • A. 120
    • B. 180
    • C. 160
    • D. 140
    • Discuss
    • 6. 
      Find the LCM of 1/3, 2/9, 5/6 and 4/27.

    • Options
    • A. 1/54
    • B. 10/27
    • C. 20/3
    • D. 3/20
    • Discuss
    • 7. 
      A runs 1 3? 8 times as fast as B. If A gives B a start of 120 m and they reach the goal at the same time, the goal is at a distance of:

    • Options
    • A. 360 m
    • B. 440 m
    • C. 460 m
    • D. 380 m
    • Discuss
    • 8. 
      124.35 % 8096 =?

    • Options
    • A. 2000
    • B. 10000
    • C. 1000
    • D. 12000
    • Discuss
    • 9. 
      Given that log 10 2 = 0.3010 the value of log 10 5 is?

    • Options
    • A. 0.3241
    • B. 0.6911
    • C. 0.6990
    • D. 0.7525
    • Discuss
    • 10. 
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    • Options
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