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

Question 1208841: Find the real solutions of the equation.

x^6 + 8•sqrt{x^(8)} = 0

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

Equation 

     +  = 0


is equivalent to

     +  = 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.

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