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?

# Let ${a}_{1}$, ${a}_{2}$, ${a}_{3}$, ${a}_{4}$ be real numbers such that ${{a}^{2}}_{1}$+${{a}^{2}}_{2}$+${{a}^{2}}_{3}$+${{a}^{2}}_{4}$ = 1. Then, the smallest possible value of the expression +  + + 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, ${{a}^{2}}_{1}$+${{a}^{2}}_{2}$+${{a}^{2}}_{3}$+${{a}^{2}}_{4}$ = 1
the smallest possible value of the expression +  + + is 0 when ${a}_{1}$= ${a}_{2}$=${a}_{3}$=${a}_{4}$= $±\frac{1}{2}$
Then, option 2 is correct.

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