What is the answer to x^{2/3}+5x^{1/3}+4=0 ?

The answer to x^{2/3}+5x^{1/3}+4=0 is x=-1,x=-64

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x^{2/3}+5x^{1/3}+4=0

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

x = - 1, x = - 64

Solution steps

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

Rewrite the equation with

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

u^{2} + 5 u + 4 = 0

Solve

u^{2} + 5 u + 4 = 0 : u = - 1, u = - 4

u = - 1, u = - 4

Substitute back

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

solve for

x

Solve

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

Solve

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

x = - 1, x = - 64

Verify Solutions:

x = - 1

True

, x = - 64

True

The solutions are

x = - 1, x = - 64

g, w = 7 - g

\frac{- 3 x + 12}{2 6 - x} = 0

- x = x^{2}

2 = - 8 + 1 + x

4 1 - x + 4 1 + x = 42

What is the answer to x^{2/3}+5x^{1/3}+4=0 ?
The answer to x^{2/3}+5x^{1/3}+4=0 is x=-1,x=-64
Solve for x: x^{2/3}+5x^{1/3}+4=0
The solution is x=-1,x=-64