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Discussion :: Square Root and Cube Root

  1.  
    If x = √3 + 1 and y = √3 - 1 , then the value of (x2 + y2) is:
    √3 - 1 √3 + 1
    2. A.
    10
    B.
    13
    C.
    14
    D.
    15

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    Answer : Option C

    Explanation :

     

    x = (√3 + 1) x (√3 + 1) = (√3 + 1)2 = 3 + 1 + 2√3 = 2 + √3.
    (√3 - 1) (√3 + 1) (3 - 1) 2
    y = (√3 - 1) x (√3 - 1) = (√3 - 1)2 = 3 + 1 - 2√3 = 2 - √3.
    (√3 + 1) (√3 - 1) (3 - 1) 2

     x2 + y2 = (2 + √3)2 + (2 - √3)2

       = 2(4 + 3)

       = 14

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