How do you solve and check for extraneous solutions in root3(x-3) =1?

1 Answer
Alan P.
Aug 7, 2015

x=4 with no extraneous solutions

Explanation:

Given root(3)(x-3) = 1

Cube both sides:
color(white)("XXXX")x-3 = 1^3 = 1

Add 3 to both sides
color(white)("XXXX")x = 4

Verify by substituting 4 for x in the original expression
color(white)("XXXX")root(3)(4-3) = root(3)(1) = 1
so this solution is not extraneous

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