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=27,x=8

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

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

x = 27, x = 8

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 = 3, u = 2

u = 3, u = 2

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 27, x = 8

Verify Solutions:

x = 27

True

, x = 8

True

The solutions are

x = 27, x = 8

4 x - 15 = x - 3

2 4 x + 5 = 8 - x - 1

4 x + 4 - 2 = 4

16 x^{2} = 2 x

y = 10

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=27,x=8
Solve for x: x^{2/3}-5x^{1/3}+6=0
The solution is x=27,x=8