Question 493431: find all solutions of the equation...
27x^3-512=0
i know i have to get the cube or something like that
or the GCF? Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given:
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First, move the -512 to the other side of the equation by adding +512 to both sides as follows:
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On the left side the -512 and the +512 total zero. Therefore, you are left with the following equation:
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Solve for by dividing both sides by 27 and you get:
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Now note that 512 is equal to 8 cubed. Also note that 27 is equal to 3 cubed. You can verify these two statements by using a calculator to first multiply 8 times 8 times 8 to get 512. Then use it to multiply 3 times 3 times 3 and you get 27. So by substituting 8 cubed for 512 and 3 cubed for 27, you can write the equation as:
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By the power rule of exponents you can furthermore write the right side of this equation as shown:
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Now solve for x by taking the cube root of both sides to get:
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which simplifies to:
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You can check this answer by returning to the equation that you were originally given and substitute for x. You should then see that:
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becomes (after cubing the ):
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and by cancelling the 27 in the numerator with the 27 in the denominator, this equation reduces to:
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Since the left side does equal the right side, the answer that is correct.
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Hope this helps you to see how to do this problem.
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