SOLUTION: (y+4) ^2/3=-2 Where y is a real number and simplify! Thank You! :)?

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Question 1015213: (y+4) ^2/3=-2
Where y is a real number and simplify!
Thank You! :)?
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


root%283%2C%28y%2B4%29%5E2%29%22%22=%22%22-2

There can be no solution because that's the cube root 
of a non-negative number, which is a non-negative
number, and so a non-negative number cannot equal to
the negative number -2.

Answer: no solution

Edwin

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Raise both sides to the third power



Expand the squared binomial



Put the quadratic in standard form



but the discriminant, is negative



So the set of real number solutions to




is the empty set.

This result squares with an intuitive analysis of the original problem. Whenever a fractional exponent has an even numerator, the result of raising to that power must be positive. Hence, the LHS of the original equation can never be negative, much less -2.

John

My calculator said it, I believe it, that settles it