∵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