B boseph158 New member Joined Jun 11, 2010 Messages 1 Jun 11, 2010 #1 All I need help with is getting started, it has been awhile since I've done one of these problems. Thanks. (1)/(1+sqrt(3)-sqrt(5))
All I need help with is getting started, it has been awhile since I've done one of these problems. Thanks. (1)/(1+sqrt(3)-sqrt(5))
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Jun 11, 2010 #2 \(\displaystyle \frac{1}{1+\sqrt{3}-\sqrt{5}}\) Multiply top and bottom by \(\displaystyle 2\sqrt{15}+\sqrt{5}+3\sqrt{3}+7\) This will eliminate the radicals in the denominator.
\(\displaystyle \frac{1}{1+\sqrt{3}-\sqrt{5}}\) Multiply top and bottom by \(\displaystyle 2\sqrt{15}+\sqrt{5}+3\sqrt{3}+7\) This will eliminate the radicals in the denominator.
B BigGlenntheHeavy Senior Member Joined Mar 8, 2009 Messages 1,577 Jun 11, 2010 #3 \(\displaystyle My \ way.\) \(\displaystyle \frac{1}{1+\sqrt3-\sqrt5}*\frac{1-\sqrt3+\sqrt5}{1-\sqrt3+\sqrt5} \ = \ \frac{1-\sqrt3+\sqrt5}{2\sqrt{15}-7}\) \(\displaystyle Hence, \ \frac{1-\sqrt3+\sqrt5}{2\sqrt{15}-7}* \ \frac{2\sqrt{15}+7}{2\sqrt{15}+7} \ = \ \frac{7+3\sqrt3+\sqrt5+2\sqrt{15}}{11}\)
\(\displaystyle My \ way.\) \(\displaystyle \frac{1}{1+\sqrt3-\sqrt5}*\frac{1-\sqrt3+\sqrt5}{1-\sqrt3+\sqrt5} \ = \ \frac{1-\sqrt3+\sqrt5}{2\sqrt{15}-7}\) \(\displaystyle Hence, \ \frac{1-\sqrt3+\sqrt5}{2\sqrt{15}-7}* \ \frac{2\sqrt{15}+7}{2\sqrt{15}+7} \ = \ \frac{7+3\sqrt3+\sqrt5+2\sqrt{15}}{11}\)
