How does it say that Cauchy Schwartz is applied here?

Question

I was going through some questions and I came across this:

I am unable to comprehend how is Cauchy Schwartz's inequality applied to the function and what does it seem to imply. As far as I know, Cauchy Schwartz's inequality states that the inner product of two vectors is less than equal to the product of the norm of those vectors.

Please shed some light on how Cauchy Schwartz's inequality is applied on the image attached.

Answer 1

$ac+bd= \langle (a,b), (c,d) \rangle \leq \sqrt {a^{2}+b^{2}}\sqrt {c^{2}+d^{2}}$.
Take $a=b=1, c=x$ and $d=y$ and proceed