Hello I wanted to know if someone can correct this exercise?

Theorem 1.1 (Cauchy-Schwarz Inequality): Consider a Euclidean vector space E, and two vectors x and y in this space. The Cauchy- Schwarz inequality can be expressed as follows: For any x and y in E, the Cauchy-Schwarz inequality states that the absolute value of the dot product of x and y is always less than or equal to the product of the norms of x and y. In other words, this means: Furthermore, equality in this inequality is achieved only when the vectors x and y are collinear, meaning they lie in the same direction. Exercise 1.3: (i) To prove this theorem, let's consider a function f(t) defined from the real numbers (R) to real numbers (R), such that f(t) = /x + tyl^2. We will show that this function is a second-degree polynomial in t and examine its sign and discriminant. (ii) Let's prove the parallelogram identity: For x and y, two vectors in space E, we have: 1/ 2 + y 1 12 + 1/20 - 31 12 = 2(1/ 201 12 + 1/31 12 ) G Regener