What is the answer to z^{2/3}+2z^{1/3}-8=0 ?

The answer to z^{2/3}+2z^{1/3}-8=0 is z=8,z=-64

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z^{2/3}+2z^{1/3}-8=0

z^{\frac{2}{3}} + 2 z^{\frac{1}{3}} - 8 = 0

z = 8, z = - 64

Solution steps

z^{\frac{2}{3}} + 2 z^{\frac{1}{3}} - 8 = 0

Use the following exponent property

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

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

(z^{\frac{1}{3}})^{2} + 2 z^{\frac{1}{3}} - 8 = 0

Rewrite the equation with

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

u^{2} + 2 u - 8 = 0

Solve

u^{2} + 2 u - 8 = 0 : u = 2, u = - 4

u = 2, u = - 4

Substitute back

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

solve for

z

Solve

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

Solve

z^{\frac{1}{3}} = - 4 : z = - 64

z = 8, z = - 64

Verify Solutions:

z = 8

True

, z = - 64

True

The solutions are

z = 8, z = - 64

1 + x + \frac{a x}{1 + x} = 0

2 x - 3 x - 2 = 0

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

x, x + 15 + x = 15

40 - x^{2} = 3 x

What is the answer to z^{2/3}+2z^{1/3}-8=0 ?
The answer to z^{2/3}+2z^{1/3}-8=0 is z=8,z=-64
Solve for z: z^{2/3}+2z^{1/3}-8=0
The solution is z=8,z=-64