My Math Forum Algebra problem. I'm stuck!

 Algebra Pre-Algebra and Basic Algebra Math Forum

 January 18th, 2012, 05:24 AM #1 Newbie   Joined: Jan 2012 Posts: 4 Thanks: 0 Algebra problem. I'm stuck! Hello. Is given: $R=\sqrt[3]{-8}+\sqrt{\sqrt{81}}-\frac{2(\sqrt2+1)}{2+\sqrt2}\;\;\;\;\text{find:}\; R^{-1}=?$ Attempted: $\sqrt[3]{-8}=\sqrt[3]{(-2)^3}=-2$ $\sqrt{\sqrt{81}}=\sqrt{9}=3$ $\frac{2(\sqrt2+1)}{2+\sqrt2}=\frac{2(\sqrt2+1)}{2+ \sqrt2}*\frac{2-\sqrt2}{2-\sqrt2}=\frac{[2(\sqrt2+1)]*(2-\sqrt2)}{4-2}=$ $\frac{(2\sqrt2+2)*(2-\sqrt2)}{2}=$$\frac{4\sqrt2-2\sqrt2\sqrt2+4-2\sqrt2}{2}=\frac{4\sqrt2-2*2+4-2\sqrt2}{2}=$ $\frac{2(2\sqrt2-\sqrt2)}{2}=2\sqrt2-sqrt2=sqrt2$ -------------------------------------------------------------------------------- $R=-2+3-\sqrt2\;\;\;\Longrightarrow\;\;\;R=1-\sqrt2$ $R^{-1}=??$ what to do now?? Thank you.
 January 18th, 2012, 05:48 AM #2 Member   Joined: Jan 2012 Posts: 80 Thanks: 0 Re: Algebra problem. I'm stuck! $R^{-1}= (1-\sqrt{2})^{-1}$ $=\frac{1}{1-\sqrt{2}}$ This may be enough or you can multiply through by $\frac{1+\sqrt{2}}{1+\sqrt{2}}$ to get $-1 - \sqrt{2}$.
January 18th, 2012, 06:56 AM   #3
Newbie

Joined: Jan 2012

Posts: 4
Thanks: 0

Re: Algebra problem. I'm stuck!

Quote:
 Originally Posted by flying_pigeon $R^{-1}= (1-\sqrt{2})^{-1}$ $=\frac{1}{1-\sqrt{2}}$ This may be enough or you can multiply through by $\frac{1+\sqrt{2}}{1+\sqrt{2}}$ to get $-1 - \sqrt{2}$.
Thanks a lot Sir.

 January 18th, 2012, 10:34 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Algebra problem. I'm stuck! A simpler way to simplify $\frac{2$$\sqrt{2}+1$$}{2+\sqrt{2}}$ would be to factor as follows: $\frac{$$\sqrt{2}$$^2$$\sqrt{2}+1$$}{\sqrt{2}$$\sqr t{2}+1$$}=\sqrt{2}$

 Tags algebra, problem, stuck

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post tucano Linear Algebra 1 December 28th, 2013 12:06 PM Kinroh Physics 2 October 1st, 2013 05:16 PM sivela Calculus 1 February 19th, 2012 10:21 PM tehroonieh md Abstract Algebra 7 December 5th, 2010 08:01 AM jordanshaw Calculus 3 October 6th, 2010 10:19 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top