How do you solve the equation and identify any extraneous solutions for $(3x^3)/4=192$ ?

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Answer 1 · 2015-06-06T23:22:43

Multiply both sides by $4/3$ to get:

$x^3 = 256 = 2^8$

This has one real solution:

$x = 2^(8/3) = 4root(3)(4)$

In case you are curious, the other two complex roots are:

$4omega root(3)(4)$ and $4omega^2 root(3)(4)$

where $omega = -1/2+sqrt(3)/2i$

is called the primitive cube root of unity.

$omega$ features in general solutions of cubic equations.

How do you solve the equation and identify any extraneous solutions for (3x^3)/4=192(3x^3)/4=192?