SOLUTION: Find the real solutions of the equation. x^6 + 8•sqrt{x^(8)} = 0

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Question 1208841: Find the real solutions of the equation.

x^6 + 8•sqrt{x^(8)} = 0


Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the real solutions of the equation.
x^6 + 8•sqrt{x^(8)} = 0
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Equation 

    x%5E6 + 8%2Asqrt%28x%5E%288%29%29 = 0


is equivalent to

    x%5E6 + 8%2Ax%5E4 = 0.


For real  x,  left side is the sum of two addends that are non-negative expressions.


The sum of two non-negative addends is zero if and only if both addends are zeros.


From it, we conclude that x= 0 is the only solution to the original equation.


ANSWER.  x = 0  is the unique real solution to the given equation.

Solved.