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

The answer to x^{2/3}+2x^{1/3}-x=0 is x=0,x=-1,x=8

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x^{2/3}+2x^{1/3}-x=0

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

x = 0, x = - 1, x = 8

Solution steps

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

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

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

Rewrite the equation with

x^{\frac{1}{3}} = u

u^{2} + 2 u - u^{3} = 0

Solve

u^{2} + 2 u - u^{3} = 0 : u = 0, u = - 1, u = 2

u = 0, u = - 1, u = 2

Substitute back

u = x^{\frac{1}{3}},

solve for

x

Solve

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

Solve

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

Solve

x^{\frac{1}{3}} = 2 : x = 8

x = 0, x = - 1, x = 8

Verify Solutions:

x = 0

True

, x = - 1

True

, x = 8

True

The solutions are

x = 0, x = - 1, x = 8

5 x + 5 = 9 - 3 x + 4

3 (x - 4)^{\frac{1}{2}} = (3 x - 12)^{\frac{1}{2}}

4 - x + y + 8 = y + 1

3 x + 4 + x - 4 = 2 x

(7 b^{0.15}) 8 = 2

What is the answer to x^{2/3}+2x^{1/3}-x=0 ?
The answer to x^{2/3}+2x^{1/3}-x=0 is x=0,x=-1,x=8
Solve for x: x^{2/3}+2x^{1/3}-x=0
The solution is x=0,x=-1,x=8