SOLUTION: Find all real solutions to each equation or inequality. For the inequalities, also sketch the graph of the solution set. 8x^3 -27=0

Algebra ->  Inequalities -> SOLUTION: Find all real solutions to each equation or inequality. For the inequalities, also sketch the graph of the solution set. 8x^3 -27=0      Log On


   

Question 169340: Find all real solutions to each equation or inequality. For the
inequalities, also sketch the graph of the solution set.
8x^3 -27=0
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E3-27=0
add 27 to both sides of the equation:
8x%5E3=27
divide both sides of equation by 8:
x%5E3=%2827%2F8%29
take cube root of both sides of equation:
root%283%2C%28x%5E3%29%29=root%283%2C%2827%2F8%29%29
which is the same as:
root%283%2C%28x%5E3%29%29=root%283%2C%2827%29%29%2Froot%283%2C%288%29%29
which becomes:
x=%283%2F2%29
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original equation is:
8x%5E3-27=0
substituting (3/2) for x in original equation gets:
%288%2A%283%2F2%29%5E3%29-27=0
which is the same as:
%288%2A%283%29%5E3%2F%282%29%5E3%29-27=0
which becomes:
%288%2A27%2F8%29-27=0
which becomes:
27-27=0
which becomes:
27=27
which is true proving that x = (3/2) is the correct answer.