How do you solve then check for extraneous solutions: $(x+5)^(2/3)=4$ ?

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Answer 1 · 2018-03-25T13:19:36

$x=3$

Raise both sides to the power of $3/2$

$((x+5)^(2/3))^(3/2) = 4^(3/2)$

$x+5 = (+-sqrt4)^3$

There are two possible solutions for $sqrt4$

$x+5 = (+2)^3" "or" "x+5 = (-2)^3$

$" "x+5 = 8" "or" "x+5 = -8$

$x = 8-5" "or" "x = -8-5$

$x = 3 or x=-13$

Check both in the original equation.

$(3+5)^(2/3) = 8^(2/3) = 4$

$(13+5)^(2/3) = 13^(2/3) =1.768" "larr$ this does not give $4$

How do you solve then check for extraneous solutions: (x+5)^(2/3)=4(x+5)^(2/3)=4?