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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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usingSolve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$
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 +/-$\sqrt(1/8)$
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.