What is the answer to 2x^{2/3}-5x^{1/3}=12 ?

The answer to 2x^{2/3}-5x^{1/3}=12 is x=64,x=-27/8

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2x^{2/3}-5x^{1/3}=12

2 x^{\frac{2}{3}} - 5 x^{\frac{1}{3}} = 12

x = 64, x = - \frac{27}{8}

Decimal Notation

x = 64, x = - 3.375

Solution steps

2 x^{\frac{2}{3}} - 5 x^{\frac{1}{3}} = 12

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} - 5 x^{\frac{1}{3}} = 12

Rewrite the equation with

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

2 u^{2} - 5 u = 12

Solve

2 u^{2} - 5 u = 12 : u = 4, u = - \frac{3}{2}

u = 4, u = - \frac{3}{2}

Substitute back

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

solve for

x

Solve

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

Solve

x^{\frac{1}{3}} = - \frac{3}{2} : x = - \frac{27}{8}

x = 64, x = - \frac{27}{8}

Verify Solutions:

x = 64

True

, x = - \frac{27}{8}

True

The solutions are

x = 64, x = - \frac{27}{8}

8 - 2 x = 1 + 5 - x

\frac{5}{2 5 x - 1} = \frac{5}{9}

x - 7 + 12 = 28

x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} - 4 = 0

x + 5 = x - 7

What is the answer to 2x^{2/3}-5x^{1/3}=12 ?
The answer to 2x^{2/3}-5x^{1/3}=12 is x=64,x=-27/8
Solve for x: 2x^{2/3}-5x^{1/3}=12
The solution is x=64,x=-27/8