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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. 
      A can complete a piece of work in 10 days, while B alone can complete it in 15 days. They work together for 5 days and rest of the work is done by C in 2 days. If they receive $ 450 for the whole work, how should they divide the money?

    • Options
    • A. $250, $100, $100
    • B. $225, $150, $75
    • C. $200, $150, $100
    • D. $175, $175, $100
    • Discuss
    • 2. 
      The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is :

    • Options
    • A. 50 ?3 m
    • B. 50 m ?3
    • C. 75 ?3 m
    • D. 75 m ?3
    • Discuss
    • 3. 
      If 30% of A = 20 % of B, then find the value of A : B?

    • Options
    • A. 1 : 3
    • B. 3 : 2
    • C. 3 : 1
    • D. 2 : 3
    • Discuss
    • 4. 80 litre mixture of milk and water contains 10% milk. How much milk (in litres) must be added to make water percentage in the mixture as 80%?

    • Options
    • A. 8
    • B. 9
    • C. 10
    • D. 12
    • Discuss
    • 5. 
      If log 5 (x 2 + x) - log 5 x = 2 then the value of x is?

    • Options
    • A. 24
    • B. 25
    • C. 23
    • D. 120
    • Discuss
    • 6. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

    • Options
    • A. 0
    • B. 1
    • C. 10
    • D. 19
    • Discuss
    • 7. 
      Two trains A and B travel from points X to Y and the ratio of the speeds of A to that of B is 2 : 7. Find the ratio of time taken by A and B to reach From X to Y.

    • Options
    • A. 2 : 5
    • B. 3 : 5
    • C. 3 : 8
    • D. 7 : 2
    • Discuss
    • 8. 
      Walking with 3/4 of his usual speed, Sachin covers a certain distance in 2 h more than the time he takes to cover the distance at his usual speed. Find the time taken by him to cover this distance with usual speed.

    • Options
    • A. 5 h
    • B. 6 h
    • C. 9 h
    • D. 4 h
    • Discuss
    • 9. 
      If ? 2 n = 64, then the value of n is?

    • Options
    • A. 2
    • B. 4
    • C. 6
    • D. 12
    • Discuss
    • 10. 
      Ram and Sita are walking towards each other with the speed of 8 km/h and 2 km/h, respectively over a road 160 km long. How soon will they meet?

    • Options
    • A. 16 h
    • B. 8 h
    • C. 10 h
    • D. 20 h
    • Discuss


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