Let a1,a2,a3,a4 be real numbers such that a1+a2+a3+a4=0 and a21+a22+a2 – InterviewSolution

1.	Let a1,a2,a3,a4 be real numbers such that a1+a2+a3+a4=0 and 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 the interval
Answer» Let $a_{1}, a_{2}, a_{3}, a_{4}$ be real numbers such that $a_{1} + a_{2} + a_{3} + a_{4} = 0$ and $a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} = 1$ . Then the smallest possible value of the expression $(a_{1} - a_{2})^{2} + (a_{2} - a_{3})^{2} + (a_{3} - a_{4})^{2} + (a_{4} - a_{1})^{2}$ lies in the interval

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