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.