find x or shorten the equation ?

I have some more questions please help me today and tomorrow !!

You guys please help me TT

Give equation  \(\sqrt{x-3-2\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}=m\)

a) Solve the equation with m = 1.

b) With which condition of x will the given equation have solution(s) ?

Prove that :

With a,b are real interger numbers we have : 

\(\dfrac{1}{a}+\dfrac{1}{b}\ge\dfrac{4}{a+b}\)

Give a,b are two real intergers \(a\ge-\dfrac{1}{4},b\ge-\dfrac{1}{4},a+b=1\)

Prove : \(\sqrt{4a+1}+\sqrt{4b+1}\le\sqrt{12}\)