If a1- a2- a3- - an- R then x-a12-x-a22-x-an2 assumes least value at x-

The correct option is D (a_1+a_2+…+a_n)/n y = (x a_1)^2+(x a_2)^2 ............ (x a_n)^2 y' = 0 2(x a_1)+2(x a_2)............2(x a_n) ...

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Byju's Answer

Standard XII

Mathematics

Global Maxima

If a1, a2, ...

Question

If $a_{1}, a_{2}, a_{3}, \dots a_{n} \in R$ then $(x - a_{1})^{2} + (x - a_{2})^{2} + \dots (x - a_{n})^{2}$ assumes least value at $x =$

a_{1} + a_{2} + a_{3} + . . . + a_{n}

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a_{n}

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n (a_{1} + a_{2} + \dots + a_{n})

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\frac{(a_{1} + a_{2} + \dots + a_{n})}{n}

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Solution

The correct option is D $\frac{(a_{1} + a_{2} + \dots + a_{n})}{n}$
$y = (x - a_{1})^{2} + (x - a_{2})^{2}$ ............ $(x - a_{n})^{2}$
$y^{'} = 0$
$2 (x - a_{1}) + 2 (x - a_{2}) . . . . . . . . . . . .2 (x - a_{n}) = 0$
$n (x) - (a_{1} + a_{2} . . . . . . . . . . a_{n}) = 0$
$x = \frac{a_{1} + a_{2} . . . . . . . . . a_{n}}{n}$

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