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=8,x=-64

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

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

x = 8, x = - 64

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 = 2, u = - 4

u = 2, u = - 4

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 8, x = - 64

Verify Solutions:

x = 8

True

, x = - 64

True

The solutions are

x = 8, x = - 64

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

x = 0.25

x, z = x (x^{2} + y^{2})^{\frac{1}{2}}

5 x - 6 = - 1

a - 1 = 7 - a

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=8,x=-64
Solve for x: x^{2/3}+2x^{1/3}-8=0
The solution is x=8,x=-64