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

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

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

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

x = 8, x = - \frac{1}{8}

Decimal Notation

x = 8, x = - 0.125

Solution steps

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

Use the following exponent property

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

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

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

Rewrite the equation with

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

2 u^{2} - 3 u = 2

Solve

2 u^{2} - 3 u = 2 : u = 2, u = - \frac{1}{2}

u = 2, u = - \frac{1}{2}

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 8, x = - \frac{1}{8}

Verify Solutions:

x = 8

True

, x = - \frac{1}{8}

True

The solutions are

x = 8, x = - \frac{1}{8}

3 x + 1 - x = - 3

49 - x^{2} - 25 - x^{2} = 3

x^{2} - 17 x - 16 x = 0

2 x + 5 - \frac{3}{2 x + 5} = - 2

\frac{- x}{25 - x ^{2}} = \frac{1}{2}

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