When x=____ The function f (x) = (x-a1) ^ 2 + (x-a2) ^ 2 +. + (x-an) ^ 2 takes the minimum value

When x=____ The function f (x) = (x-a1) ^ 2 + (x-a2) ^ 2 +. + (x-an) ^ 2 takes the minimum value

f(x)=nx²-2（a1+a2+…… an）x+a1²+a2²+…… F (x) = n (X & sup2; - 2 (a1 +...) an）x/n+（a1+a2+…… an）²/n²）+a1²+…… an²-（a1+a2+…… an）²/n=n(x-(a1+…… a...

2. When the value of X is, the function y = (x-a1) 2 + (x-a2) 2 + +(x-an) 2 is the minimum

Y = (x-a1) ^ 2 + (x-a2) ^ 2. +. + (x-an) ^ 2 = x ^ 2-2a1x + A1 ^ 2 + x ^ 2-2a2x + A2 ^ 2... + x ^ 2-2anx + an ^ 2 = NX ^ 2-2 (a1 + A2 + a3... + an) x + (A1 ^ 2 + A2 ^ 2 + a3 ^ 2... + an ^ 2) the abscissa of the minimum value of this quadratic function is 2 (a1 + A2... + an) / 2n = (a1 + A2 + a3... + an) / N, that is, x = (a1 + A2

When x is the value, the function f (x) = (x-a1) 62 + (x-a2) ^ 2 +. + (x-an) ^ 2 takes the minimum value
When x is the value, the function f (x) = (x-a1) ^ 2 + (x-a2) ^ 2 +... + (x-an) ^ 2 takes the minimum value
1 in A1 is the pin code.
a2
The same goes for an

A1, A2 are constants, which are equivalent to 1,2,3. Expand f (x)
nx^2-2(a1+a2+...+an)x+a1^2+a2^2+...an^2
It's a parabola with an opening up, and then the formula comes to the minimum of X on the axis of symmetry
X = (a1 + A2 +... + an) / N is the smallest
So Do you understand? If not, hi me