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

The answer to x^{2/3}-4x^{1/3}-5=0 is x=125,x=-1

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

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

x = 125, x = - 1

Solution steps

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

Rewrite the equation with

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

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

Solve

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

u = 5, u = - 1

Substitute back

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

solve for

x

Solve

x^{\frac{1}{3}} = 5 : x = 125

Solve

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

x = 125, x = - 1

Verify Solutions:

x = 125

True

, x = - 1

True

The solutions are

x = 125, x = - 1

(8 x)^{\frac{4}{3}} + 44 = 300

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

x + 22 = x + 2

x - 3 = x + 3

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

What is the answer to x^{2/3}-4x^{1/3}-5=0 ?
The answer to x^{2/3}-4x^{1/3}-5=0 is x=125,x=-1
Solve for x: x^{2/3}-4x^{1/3}-5=0
The solution is x=125,x=-1