How do you solve $x^3=4x$ ?

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Answer 1 · 2016-06-09T10:33:15

$x = 0, " or "x= -2," or " x= 2$

the tempting method is just to divide by $x$ which gives
$x^2 = 4$

However in dividing by $x$ we have made an assumption that $x$ is not 0, in which case it would not be allowed.

Make the equation = 0: $" " x^3 - 4x = 0$

Factorise fully: $" " x(x^2 -4) = 0$

So, $x(x + 2)(x - 2) = 0$

Each factor can be equal to 0, so
$x = 0, " or "x= -2," or " x= 2$

An equation with $x^3$ should have 3 solutions, which we have.

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