Can you Solve Oxford University Admission Interview Algebra ?

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  • เผยแพร่เมื่อ 10 พ.ย. 2024
  • University Admission Exam Question || Algebra Problem || Entrance Aptitude Simplification Test || Tricky Interview
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ความคิดเห็น • 3

  • @RealQinnMalloryu4
    @RealQinnMalloryu4 หลายเดือนก่อน

    (xy ➖ 4xy+3). (xy ➖ 3xy+2).

  • @key_board_x
    @key_board_x หลายเดือนก่อน +2

    Without introducing variable m & n
    x + xy - y = 7 ← equation (1)
    x + xy - y - 1 = 7 - 1
    x + xy - y - 1 = 6
    x²y - xy² = 6 ← equation (1)
    x²y - xy² = 6 → we've just seen that: x + xy - y - 1 = 6
    x²y - xy² = x + xy - y - 1
    x²y - xy² - x - xy + y + 1 = 0
    x²y - xy² - xy - x + y + 1 = 0
    xy.(x - y - 1) - (x - y - 1) = 0
    (xy - 1).(x - y - 1) = 0
    First possibility: (xy - 1) = 0
    xy - 1 = 0
    xy = 1
    y = 1/x ← memorize this result
    From equation (1)
    x + xy - y = 7 → where: xy = 1
    x + 1 - y = 7
    x - y = 6 → recall: y = 1/x
    x - (1/x) = 6
    (x² - 1)/x = 6
    x² - 1 = 6x
    x² - 6x - 1 = 0
    Δ = (- 6)² - (4 * - 1) = 36 + 4 = 40 = 4 * 10
    x = (6 ± 2√10)/2
    x = 3 ± √10
    First solution: x = 3 + √10
    Recall: y = 1/x
    y = 1/(3 + √10)
    y = (3 - √10)/[(3 + √10).(3 - √10)]
    y = (3 - √10)/[9 - 10]
    y = (3 - √10)/(- 1)
    y = - 3 + √10
    Second solution: x = 3 - √10
    Recall: y = 1/x
    y = 1/(3 - √10)
    y = (3 + √10)/[(3 - √10).(3 + √10)]
    y = (3 + √10)/[9 - 10]
    y = (3 + √10)/(- 1)
    y = - 3 - √10
    Second possibility: (x - y - 1) = 0
    x - y - 1 = 0
    y = x - 1 ← memorize this result
    From equation (1)
    x + xy - y = 7 → where: y = x - 1
    x + x.(x - 1) - (x - 1) = 7
    x + x² - x - x + 1 = 7
    x² - x - 6 = 0
    Δ = (- 1)² - (4 * - 6) = 1 + 24 = 25 = 5²
    x = (1 ± 5)/2
    x = 3 or x = - 2
    Third solution: x = 3
    Recall: y = x - 1
    y = 3 - 1
    y = 2
    Fourth solution: x = - 2
    Recall: y = x - 1
    y = - 2 - 1
    y = - 3
    Resume solution (x ; y)
    (3 + √10 ; - 3 + √10)
    (3 - √10 ; - 3 - √10)
    (3 ; 2)
    (- 2 ; - 3)