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    Question

    If x2 - 7x + 1 = 0, then find the value

    of: 3 + ( x 6 +  x 4 +  x 2 + 1)/ 7x 3    
    A 55 Correct Answer Incorrect Answer
    B 64 Correct Answer Incorrect Answer
    C 36 Correct Answer Incorrect Answer
    D 50 Correct Answer Incorrect Answer

    Solution

    Given, x2 - 7x + 1 = 0 Or, x2 + 1 = 7x - [I] x  + 1/x = 7  - [II] = 3 + ( x 6 +  x 4 +  x 2 + 1)/ 7x 3     = 3 + { x 4( x 2 + 1) + ( x 2 + 1)}/( x 2 + 1) x 2  = 3 +  ( x 2 + 1) + ( x 4 + 1)}/( x 2 + 1) x 2 = 3 + ( x 4 + 1)/ x 2 = 3 + x 2 + 1/ x 2 On squaring equation [II] x2  + 1/x2 + 2 = 49 Adding '1' both sides, we get x2  + 1/x2  + 3 = 50

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