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

The answer to x^{2/3}-2x^{1/3}-3=0 is x=27,x=-1

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

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

x = 27, x = - 1

Solution steps

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

Rewrite the equation with

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

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

Solve

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

u = 3, u = - 1

Substitute back

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

solve for

x

Solve

x^{\frac{1}{3}} = 3 : x = 27

Solve

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

x = 27, x = - 1

Verify Solutions:

x = 27

True

, x = - 1

True

The solutions are

x = 27, x = - 1

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

3 x + 4 - x - 4 = 2 x

x + 2 = 2 x - 3

5 x + 81 + 2 = 8

10 + a + 7 = 11

What is the answer to x^{2/3}-2x^{1/3}-3=0 ?
The answer to x^{2/3}-2x^{1/3}-3=0 is x=27,x=-1
Solve for x: x^{2/3}-2x^{1/3}-3=0
The solution is x=27,x=-1