If a∈R and a1,a2,a3⋯⋯,an∈R then (x−a1)2+(x−a2)2+….+(x−an)2 assumes its least value at x =

We have, (x−a1)2+(x−a2)2+……+(x−an)2 =nx2−2x(a1+a2+…+an)+(a12+a22+…+an2)Clearly, y=nx2−2x(a1+a2+….+an)+(a12+a22+…+an2)represents a parabola which opens upward. So, it attains its minimum value at the vertex ie. atx=2(a1+a2+….+an)2n=a1+a2+….+ann      Usingx=−b2a