What is the answer to x^{2/3}-5x^{1/3}-6=0 ?

The answer to x^{2/3}-5x^{1/3}-6=0 is x=216,x=-1

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x^{2/3}-5x^{1/3}-6=0

x^{\frac{2}{3}} - 5 x^{\frac{1}{3}} - 6 = 0

x = 216, x = - 1

Solution steps

x^{\frac{2}{3}} - 5 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} - 5 x^{\frac{1}{3}} - 6 = 0

Rewrite the equation with

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

u^{2} - 5 u - 6 = 0

Solve

u^{2} - 5 u - 6 = 0 : u = 6, u = - 1

u = 6, u = - 1

Substitute back

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

solve for

x

Solve

x^{\frac{1}{3}} = 6 : x = 216

Solve

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

x = 216, x = - 1

Verify Solutions:

x = 216

True

, x = - 1

True

The solutions are

x = 216, x = - 1

x - 2 = - 3

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

3 x + x + 1 = 7

x, x - 4 + 5 = 3 x + 3

x - 3 = x - 6

What is the answer to x^{2/3}-5x^{1/3}-6=0 ?
The answer to x^{2/3}-5x^{1/3}-6=0 is x=216,x=-1
Solve for x: x^{2/3}-5x^{1/3}-6=0
The solution is x=216,x=-1