Question 75636
Find the solutions of the following equations.  Check for extraneous solutions.
(x-5)^1/4+3=2
{{{(x-5)^(1/4)+3=2}}}
{{{(x-5)^(1/4)+3-3=2-3}}}
{{{(x-5)^(1/4)=-1}}}
There is no even root that results in a negative outcome, so you can stop here and say there's no solution.  However, if your teacher wants you to keep going:
{{{((x-5)^(1/4))^4=(-1)^4}}}
{{{x-5=1}}}
{{{x-5+5=1+5}}}
{{{x=6}}}
However this is extraneous, because:
{{{(6-5)^(1/4)+3=2}}}
{{{(1)^(1/4)+3=2}}}
{{{1+3=2}}}
{{{4=2}}} Not true.
Happy Calculating!!!!