What is the answer to roots x-3x^{1/3} ?

The answer to roots x-3x^{1/3} is x=0,x=-3^{3/2},x=3^{3/2}

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roots x-3x^{1/3}

roots

x - 3 x^{\frac{1}{3}}

x = 0, x = - 3^{\frac{3}{2}}, x = 3^{\frac{3}{2}}

Solution steps

x - 3 x^{\frac{1}{3}}

The roots are the intercepts with the x-axis

(y = 0)

x - 3 x^{\frac{1}{3}} = 0

Remove roots

- 27 x = - x^{3}

Solve

- 27 x = - x^{3} : x = 0, x = - 3^{\frac{3}{2}}, x = 3^{\frac{3}{2}}

x = 0, x = - 3^{\frac{3}{2}}, x = 3^{\frac{3}{2}}

Verify Solutions:

x = 0

True

, x = - 3^{\frac{3}{2}}

True

, x = 3^{\frac{3}{2}}

True

The solutions are

x = 0, x = - 3^{\frac{3}{2}}, x = 3^{\frac{3}{2}}

x - 7 - x = 7

\frac{1}{x} = x

\frac{- 2}{3 x ^{\frac{1}{3}}} = 0

x + 1 = 1 + \frac{x}{2}

2 x + 40 = - 16 - 2 x

What is the answer to roots x-3x^{1/3} ?
The answer to roots x-3x^{1/3} is x=0,x=-3^{3/2},x=3^{3/2}