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Solve in real numbers

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anemone

MHB POTW Director
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Feb 14, 2012
3,707
Solve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$
 
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kaliprasad

Well-known member
Mar 31, 2013
1,309
Solve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$
using

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


we get

$(3a)^3 = 3a(a^2-1)$
a= 0 or +/-$\sqrt(1/8)$
 

Opalg

MHB Oldtimer
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Feb 7, 2012
2,712
using

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


we get

$(3a)^3 = 3a(a^2-1)$
a= 0 or +/-$\sqrt(1/8)$
Neat 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.
 

kaliprasad

Well-known member
Mar 31, 2013
1,309
Neat 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.
There was a calculation mistake in my method
 
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anemone

MHB POTW Director
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Feb 14, 2012
3,707
Thanks to both of you for participating and yes, $a=0$ is the only answer to the problem.:)