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    Question

    If (x24  +  1)/x12  = 7, then

    the value of (x72  +  1)/x36  is 
    A 433 Correct Answer Incorrect Answer
    B 322 Correct Answer Incorrect Answer
    C 343 Correct Answer Incorrect Answer
    D 432 Correct Answer Incorrect Answer

    Solution

    (x24  +  1)/x12  = 7  ⇒  x24/x12   + 1/x12    = 7 ⇒ x12 + 1/x12     = 7  ∴ (x72  +  1)/x36  = x72/x36  + 1/x36      = x36  + 1/x36    =   (x12  + 1/x12 )3 – 3 × x12 × 1/x12    (x12  + 1/x12)    ∵ (a + b)³ = a³ + b³ + 3ab (a + b)  = 7³ - 3 × 7 = 343 – 21 = 322

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