# Surd Fraction

• Jun 26th 2013, 12:33 PM
Seaniboy
Surd Fraction
hi,
anyone got some ideas on figuring out this answer to the attached question.
Thanks
.
• Jun 26th 2013, 12:38 PM
Re: Surd Fraction
There's no question here, just a couple of equations but no statement of what to do.
• Jun 26th 2013, 01:54 PM
HallsofIvy
Re: Surd Fraction
I presume that the "question" is in the second, uncompleted, "equation".

If $\displaystyle x= \sqrt{k}+ \frac{1}{\sqrt{k}}+ 1$ then $\displaystyle x^2- 2x=$. Looks to me like its just a matter of doing the calculation.

$\displaystyle x^2= (\sqrt{k}+ \frac{1}{\sqrt{k}}+ 1)^2= (\sqrt{k}+ \frac{1}{\sqrt{k}})^2+ 2(\sqrt{k}+ \frac{1}{\sqrt{k}})+ 1$

$\displaystyle -2x= 2(\sqrt{k}+ \frac{1}{\sqrt{k}})+ 2$ so subtracting just gives
$\displaystyle (\sqrt{k}+ \frac{1}{\sqrt{k}})^2- 1$

Go ahead and multiply that square and see what you get.
• Jun 27th 2013, 07:54 AM
Seaniboy
Re: Surd Fraction
Hi,
Thank you very much for taking the time to answer this question. Apologies for failure to specify question detal,l but you nailed it. Kind regards,
Sean.