Question-88364

Question Number 88364 by Power last updated on 10/Apr/20

Answered by mind is power last updated on 10/Apr/20

b y C a u c h y s h w a r t

\underset{i = 1}{\sum^{n}} 1 . x_{i} ⩽ \sqrt{\underset{i = 1}{\sum^{n}}} 1^{2} . \sqrt{\underset{i = 1}{\sum^{n}} x_{i}^{2}}, \dots . . 1

Σ x_{i} = 1

Σ x_{i}^{2} = \frac{1}{n}

1 \Leftrightarrow 1 ⩽ \sqrt{n} . \frac{1}{\sqrt{n}} = 1 e q u a l i t y \Rightarrow b y c a u c h y s h w a r t z

(x_{1}, x_{2}, \dots ., x_{n}) = (a, a, \dots ., a)

\Rightarrow n a = 1 \Rightarrow a = \frac{1}{n}, \forall i \in {1, \dots . n} x_{i} = \frac{1}{n}