Equality condition in Cauchy-Schwarz is for all i but what happens when . When the denominator is zero it should be undefined, but zero may be an equality solution.
By multiplying by 2 on both sides and a little rearrangement we get
Which is true for all reals a,b,c and also equality holds when even when
We can also solve this by Cauchy-Schwarz :-
And equality holds when,
Therfore, we get, but will make the expression undefined but is also a valid solution.