How do you solve " (x-4)^3/2 = -6 "? - Math Central

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Question from Jim, a student:

How do you solve " (x-4)^3/2 = -6 "?

Hi Jim,

(x - 4)^3/2 can be written [(x - 4)³]^1/2 so in particular if x = 8 then (x - 4)^3/2 can be evaluated as

(8 - 4)^3/2 = 4^3/2 = [4³]^1/2 = 16^1/2 = 4

What I want you to notice is that the last operation I performed was a square root and the square root is never negative. Thus (x - 4)^3/2 can't possibly be -6 so your equation has no solution.

Penny

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