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

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

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x^{2/3}-2x^{1/3}-8=0

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

x = 64, x = - 8

Solution steps

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

Rewrite the equation with

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

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

Solve

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

u = 4, u = - 2

Substitute back

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

solve for

x

Solve

x^{\frac{1}{3}} = 4 : x = 64

Solve

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

x = 64, x = - 8

Verify Solutions:

x = 64

True

, x = - 8

True

The solutions are

x = 64, x = - 8

x^{2} + 5 x - 10 = 0

x + 2 x - 1 = 2

16 + x + 18 = 121

- 9 x + 10 = 3 x^{0.2}

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

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