Solve in real numbers

anemone

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

Last edited:

Well-known member
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
Staff member
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.

From $3a = 3\sqrt[3]{a(a^2-1)}$, I get $a^3 = a(a^2-1)$, with $a=0$ the only solution.
Thanks to both of you for participating and yes, $a=0$ is the only answer to the problem.