Problem: The arithmetic mean between x+ax\dfrac{x+a}{x}xx+a​ and x−ax\dfrac{x-a}{x}xx−a​, when x≠0x \neq 0xî€ =0, is (the symbol ≠\neqî€ = means "not equal to"):
Answer Choices:
A. 2 , if a ≠0\neq 0î€ =0
B. 111
C. 1 , if a=0a=0a=0 only
D. a/xa / xa/x
E. xxx Solution:
12(x+ax+x−ax)=12(2xx)=1\dfrac{1}{2}\left(\dfrac{x+a}{x}+\dfrac{x-a}{x}\right)=\dfrac{1}{2}\left(\dfrac{2 x}{x}\right)=121​(xx+a​+xx−a​)=21​(x2x​)=1