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

The answer to 2x^{2/3}+x^{1/3}-1=0 is x= 1/8 ,x=-1

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

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

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

Decimal Notation

x = 0.125, x = - 1

Solution steps

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

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

Rewrite the equation with

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

2 u^{2} + u - 1 = 0

Solve

2 u^{2} + u - 1 = 0 : u = \frac{1}{2}, u = - 1

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

Substitute back

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

solve for

x

Solve

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

Solve

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

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

Verify Solutions:

x = \frac{1}{8}

True

, x = - 1

True

The solutions are

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

x = 9 x - 10

4 - x = x - 2

2 x + 1 + 4 = - 1

What is the answer to 2x^{2/3}+x^{1/3}-1=0 ?
The answer to 2x^{2/3}+x^{1/3}-1=0 is x= 1/8 ,x=-1
Solve for x: 2x^{2/3}+x^{1/3}-1=0
The solution is x= 1/8 ,x=-1