What is the answer to x^{2/3}+x^{1/3}-6=0 ?

The answer to x^{2/3}+x^{1/3}-6=0 is x=8,x=-27

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x^{2/3}+x^{1/3}-6=0

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

x = 8, x = - 27

Solution steps

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

Rewrite the equation with

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

u^{2} + u - 6 = 0

Solve

u^{2} + u - 6 = 0 : u = 2, u = - 3

u = 2, u = - 3

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 8, x = - 27

Verify Solutions:

x = 8

True

, x = - 27

True

The solutions are

x = 8, x = - 27

7 x + 56 = x + 8

8 x - 20 = x - 1

44 - 5 x = x - 6

- 5 - 7 x + 4 + x = 7 - 6 x

8 x + 17 = x + 3

What is the answer to x^{2/3}+x^{1/3}-6=0 ?
The answer to x^{2/3}+x^{1/3}-6=0 is x=8,x=-27
Solve for x: x^{2/3}+x^{1/3}-6=0
The solution is x=8,x=-27