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

The answer to 3x^{2/3}+x^{1/3}-2=0 is x= 8/27 ,x=-1

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

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

x = \frac{8}{27}, x = - 1

Decimal Notation

x = 0.29629 \dots, x = - 1

Solution steps

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

Use the following exponent property

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

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

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

Rewrite the equation with

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

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

Solve

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

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

Substitute back

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

solve for

x

Solve

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

Solve

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

x = \frac{8}{27}, x = - 1

Verify Solutions:

x = \frac{8}{27}

True

, x = - 1

True

The solutions are

x = \frac{8}{27}, x = - 1

x + 14 - 2 x + 5 = 1

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

y, x + y + 2 = 2 x + 2 y

x - 3 = 4 x - 7

What is the answer to 3x^{2/3}+x^{1/3}-2=0 ?
The answer to 3x^{2/3}+x^{1/3}-2=0 is x= 8/27 ,x=-1
Solve for x: 3x^{2/3}+x^{1/3}-2=0
The solution is x= 8/27 ,x=-1