MathematicsLet a1, a2, a3, a4 be real numbers such that a21+a22+a23+a24 = 1. Then, the smallest possible value of the expression (a1- a2)2 +  ( a2- a3)2+ (a3- a4)2+(a4- a1)2 lies in which interval?

Let a1, a2, a3, a4 be real numbers such that a21+a22+a23+a24 = 1. Then, the smallest possible value of the expression (a1- a2)2 +  ( a2- a3)2+ (a3- a4)2+(a4- a1)2 lies in which interval?


  1. A
    0
  2. B
    -1.5
  3. C
    3.5
  4. D
    2 

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    Solution:

    Given that, a21+a22+a23+a24 = 1
    the smallest possible value of the expression (a1- a2)2 +  ( a2- a3)2+ (a3- a4)2+(a4- a1)2 is 0 when a1= a2=a3=a4= ±12
    Then, option 2 is correct.
     
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