Let f(x)=(x^2+3)/(2x) for x not equal to 0. Show that if x>3^(1/2), then f(x)>3^(1/2)

Hi, this exercise is giving headaches :(. I only need help with Part A because I know part B and have an idea of how to solve other exercises similar to part C. Thanks a lot!

The whole exercise says:

"Let for . Define a sequence of real numbers by

for , .

A) Show that if , then .

B) Show that if , then .

C) Conclude that the sequence converges."

Re: Let f(x)=(x^2+3)/(2x) for x not equal to 0. Show that if x>3^(1/2), then f(x)>3^(

A) Note that . Furthermore, , which is always positive when . Hence, the minimal value of is , or .

Therefore for all .

Re: Let f(x)=(x^2+3)/(2x) for x not equal to 0. Show that if x>3^(1/2), then f(x)>3^(

Thanks! I didn't even think it could be solved so easily *sigh*