anemone said:Solve 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.kaliprasad said: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 said:Neat method, but I get a different answer.
[sp]From $3a = 3\sqrt[3]{a(a^2-1)}$, I get $a^3 = a(a^2-1)$, with $a=0$ the only solution.[/sp]
The equation is asking to solve for the value of "a" that would make the sum of the three cube roots equal to zero.
There are two possible solutions for this equation in real numbers: a=-1 and a=1.
To solve this equation, you can use the properties of cube roots to rewrite it as (a-1)^(1/3) + (a)^(1/3) + (a+1)^(1/3) = 0. Then, you can use a substitution method or trial and error to find the possible values of "a" that would make the equation equal to zero.
Yes, you can also graph the equation and find the x-intercepts, which would give you the solutions for "a". Additionally, you can use a calculator or a computer program to solve for the solutions numerically.
Solving this equation can help in finding the values of "a" that would satisfy the given expression, which can be useful in solving other mathematical problems or in understanding the behavior of the given equation. It also helps in developing problem-solving skills and deepening the understanding of algebraic concepts.