Question 44817
f(a)=f(a+1) means that the function has the same value x=1 and when x=(a+1)
{{{f(x)=2/x+1/(x-1)}}}
so:
{{{2/a+1/(a-1)=2/(a+1)+1/a}}}
Now rearrange to find a:
{{{2+(a+1)/(a-1)=2(a+1)+(a+1)/a}}}
{{{2(a-1)+(a+1)=2(a+1)(a-1)+(a+1)(a-1)/a}}}
{{{2a(a-1)+(a+1)a=2a(a+1)(a-1)+(a+1)(a-1)}}}
{{{2a^2-a+a^2+a=2a(a^2-1)+(a^2-1)}}}
{{{3a^2=2a^3-2a^2+(a^2-1)}}}
{{{3a^2=2a^3-a^2-1}}}
{{{2a^3-4a^2-1=0}}}
Use this link:
http://www.1728.com/cubic2.htm
to find the root(s) of this equation.
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam