Solve 54x^3-16=0.

Dec 2009
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How do I solve for this problem

54x^3-16=0
 
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Prove It

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Aug 2008
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How do I solve for this problem

54x^3-16=0
Assuming \(\displaystyle x\) is real...

\(\displaystyle 54x^3 = 16\)

\(\displaystyle x^3 = \frac{16}{54}\)

\(\displaystyle x^3 = \frac{8}{27}\)

\(\displaystyle x = \sqrt[3]{\frac{8}{27}}\)

\(\displaystyle x = \frac{\sqrt[3]{8}}{\sqrt[3]{27}}\)

\(\displaystyle x = \frac{2}{3}\).
 
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Chris L T521

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How do I solve for this problem

54x^3-16=0
Solve for \(\displaystyle x^3\) and then take the cube root of both sides.

\(\displaystyle 54x^3-16=0\implies x^3=\frac{16}{54}=\frac{8}{27}\)

Thus, \(\displaystyle x=\sqrt[3]{\frac{8}{27}}=\ldots\).

Can you simplify this result?
 
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