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LammettHash
Isolate the root expression:

[tex]\sqrt[3]{x+1}+2=0\implies\sqrt[3]{x+1}=-2[/tex]

Take the third power of both sides:

[tex]\sqrt[3]{x+1}=-2\implies(\sqrt[3]{x+1})^3=(-2)^3[/tex]

Simplify:

[tex](\sqrt[3]{x+1})^3=(-2)^3\implies x+1=-8[/tex]

Isolate and solve for [tex]x[/tex]:

[tex]x=-9[/tex]

Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When [tex]x=-9[/tex], we have

[tex]\sqrt[3]{-9+1}=\sqrt[3]{-8}=\sqrt[3]{(-2)^3}=-2[/tex]

as required.
AlyssaSilverStone

Answer:

Isolate the root expression:

Take the third power of both sides:

Simplify:

Isolate and solve for :

Since the cube root function is bijective, we know this won't be an extraneous solution, but it doesn't hurt to verify that this is correct. When , we have

as required.

Step-by-step explanation:

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