What is the answer to x^{2/3}-3x^{1/3}-4=0 ?

The answer to x^{2/3}-3x^{1/3}-4=0 is x=64,x=-1

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x^{2/3}-3x^{1/3}-4=0

x^{\frac{2}{3}} - 3 x^{\frac{1}{3}} - 4 = 0

x = 64, x = - 1

Solution steps

x^{\frac{2}{3}} - 3 x^{\frac{1}{3}} - 4 = 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} - 3 x^{\frac{1}{3}} - 4 = 0

Rewrite the equation with

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

u^{2} - 3 u - 4 = 0

Solve

u^{2} - 3 u - 4 = 0 : u = 4, u = - 1

u = 4, u = - 1

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 64, x = - 1

Verify Solutions:

x = 64

True

, x = - 1

True

The solutions are

x = 64, x = - 1

2 x - 15 + 5 = 6

7 x + 60 + 12 = 14

y, x^{2} + y^{2} = x^{2} + y^{2}

- 1 = 6 x + 21 - x

2 x + 1 - 3 4 x - 3 - 5 = 0

What is the answer to x^{2/3}-3x^{1/3}-4=0 ?
The answer to x^{2/3}-3x^{1/3}-4=0 is x=64,x=-1
Solve for x: x^{2/3}-3x^{1/3}-4=0
The solution is x=64,x=-1