Question

Vă rog !!! Dau coroana !!!​

Answer 1

Răspuns:

Avem

$x_1x_2\ge x_2^2\\x_1x_3+x_2x_3\ge x_3^2+x_3^2=2x_3^2\\x_1x_4+x_2x_4+x_3x_4\ge 3x_4^2\\\ldots\\x_1x_n+x_2x_n+\ldots x_{n-1}x_n\ge (n-1)x_n^2$

Atunci

$(x_1+x_2+\ldots+x_n)^2=x_1^2+x_2^2+\ldots+x_n^2+2x_1x_2+2x_1x_3+2x_2x_3+\ldots=\\=x_1^2+(x_2^2+2x_1x_2)+(x_3^2+2x_1x_3+2x_2x_3)+\ldots+(x_n^2+2x_1x_n+\ldots+2x_{n-1}x_n)\ge\\\ge x_1^2+3x_2^2+5x_3^2+\ldots+(2n-1)x_n^2$

Explicație pas cu pas:

Answer 2

Răspuns:

Explicație pas cu pas: