You need to show,Originally Posted byJudi

Upon squaring we have,if and only if

If and only If

if and only if

if and only if

If and only if*)

This is true by Cauchy-Swarchz Inequality.

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Explanation of last step.

We will prove a famous case,

Because this is true only when, (take square roots)

Consider vectors in

Then,

-by Cauchy-Swartchz

But,

and,

*)If LHS is negative there is nothing to prove because RHS must be positive! We assume it is positive also.

Note: The consistent use of 'if and only if' otherwise the proof falls.