Question 370127
You found that {{{u=3-sqrt(11)}}} or {{{u=3+sqrt(11)}}}, which is completely correct. However, we want to solve for 'w'.


Recall that you let {{{u=w^2}}}. 



So plug this into the two equations above to get



{{{w^2=3-sqrt(11)}}} or {{{w^2=3+sqrt(11)}}}



Now we need to solve each equation for 'w'. We'll do this by taking the square root of both sides.



So solve {{{w^2=3-sqrt(11)}}} for w to get



{{{w=sqrt(3-sqrt(11))}}} or {{{w=-sqrt(3-sqrt(11))}}}




Now solve {{{w^2=3+sqrt(11)}}} for w to get



{{{w=sqrt(3+sqrt(11))}}} or {{{w=-sqrt(3+sqrt(11))}}}



So the four solutions are 




{{{w=sqrt(3-sqrt(11))}}}, {{{w=-sqrt(3-sqrt(11))}}}, {{{w=sqrt(3+sqrt(11))}}}, or {{{w=-sqrt(3+sqrt(11))}}}



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Jim