∵a_ 1^2+a_2^2+？ a_n^2= 1 ①

x_ 1^2+x_2^2+？ X_n^2= 1 ②

Put ①+②

get(a _ 1 ^ 2+a _ 2 ^ 2+？ a_n^2)+(x_ 1^2+x_2^2+？ X_n^2)=2

That is (a _12+x _12)+(a _ 2 2+x _ 2 2)+? +(a_n^2 +？ X_n^2)

= 2≥2a _ 1x _ 1+2a _ 2x _ 2+？ 2a_n x_n

Simplification and neatness

a_ 1 x_ 1+a_2 x_2+？ a_n x_n≤ 1