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- Feb 14, 2012

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Solve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$

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- Thread starter anemone
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- Thread starter
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- #1

- Feb 14, 2012

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Solve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$

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- Mar 31, 2013

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usingSolve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$

x+y+z=0=>$x^3+y^3+x^3 = 3xyz$

we get

$(3a)^3 = 3a(a^2-1)$

a= 0 or +/-$\sqrt(1/8)$

a= 0 or +/-$\sqrt(1/8)$

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- #3

- Feb 7, 2012

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Neat method, but I get a different answer.using

x+y+z=0=>$x^3+y^3+x^3 = 3xyz$

we get

$(3a)^3 = 3a(a^2-1)$

a= 0 or +/-$\sqrt(1/8)$

From $3a = 3\sqrt[3]{a(a^2-1)}$, I get $a^3 = a(a^2-1)$, with $a=0$ the only solution.

- Mar 31, 2013

- 1,343

There was a calculation mistake in my methodNeat method, but I get a different answer.

From $3a = 3\sqrt[3]{a(a^2-1)}$, I get $a^3 = a(a^2-1)$, with $a=0$ the only solution.

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- #5

- Feb 14, 2012

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Thanks to both of you for participating and yes, $a=0$ is the only answer to the problem.