Question 989399

Solve the equation and find extraneous solutions.

(x+5)^(2/3)=4
<pre>{{{highlight(highlight((x + 5)^(2/3) = 4))}}}
{{{highlight(highlight((x + 5)^((2/3) * (3/2)) = 4^(3/2)))}}} -------- Raising each side to the {{{3/2}}} power
{{{highlight(highlight((x + 5)^((cross(2)/cross(3)) * (cross(3)/cross(2))) = 4^(3/2)))}}}
{{{x + 5 =" " +- (sqrt(4))^3}}}
{{{x + 5 = " "+- 2^3}}}
{{{x + 5 = " " +- 8}}}
x = 8 - 5, or {{{highlight_green(x = 3)}}}	      OR	   x = - 8 - 5, or - 13 (ignore, as this is an extraneous solution)