How much does Cauchy-Schwarz Inequality can handle?

Algebra Level 3

Which of the following is the domain of ( a 1 , a 2 , … , a n ) (a_1,a_2,…,a_n ) and ( b 1 , b 2 , … , b n ) (b_1,b_2,…,b_n ) , such that we will always have

( a 1 2 + a 2 2 + ⋯ + a n 2 ) ( b 1 2 + b 2 2 + ⋯ + b n 2 ) ≥ ( a 1 b 1 + a 2 b 2 + ⋯ + a n b n ) 2 (a_1^2+a_2^2+⋯+a_n^2 )(b_1^2+b_2^2+⋯+b_n^2 )≥(a_1 b_1+a_2 b_2+⋯+a_n b_n )^2

Choose the most suitable answer.

a i , b i a_i, b_i are positive numbers. a i , b i a_i, b_i are real numbers. a i , b i a_i, b_i are non-negative numbers. a i , b i a_i, b_i are complex numbers.

Christopher Boo by Christopher Boo , 24, Singapore

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