If a∈R and a1,a2,a3…,an∈R then x−a12+x−a22+…+x−an2 assumes its least value at x=

We have,  x−a12+x−a22+……+x−an2= nx2−2xa1+a2+….+an+a12+a22+….+an2Clearly, y=nx2−2xa1+a2+….+an+a12+a22+….+an2represents a parabola which opens upward. So, it attains its minimum value at the vertex i.e. atx=2a1+a2+….+an2n=a1+a2+…..+ann [Using x=−b2a