What is the answer to x^{2/3}-7x^{1/3}+10=0 ?

The answer to x^{2/3}-7x^{1/3}+10=0 is x=125,x=8

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x^{2/3}-7x^{1/3}+10=0

x^{\frac{2}{3}} - 7 x^{\frac{1}{3}} + 10 = 0

x = 125, x = 8

Solution steps

x^{\frac{2}{3}} - 7 x^{\frac{1}{3}} + 10 = 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} - 7 x^{\frac{1}{3}} + 10 = 0

Rewrite the equation with

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

u^{2} - 7 u + 10 = 0

Solve

u^{2} - 7 u + 10 = 0 : u = 5, u = 2

u = 5, u = 2

Substitute back

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

solve for

x

Solve

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

Solve

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

x = 125, x = 8

Verify Solutions:

x = 125

True

, x = 8

True

The solutions are

x = 125, x = 8

\frac{5}{6} x^{- \frac{1}{6}} = 1

3 x - 2 x^{2} + 9 = 0

3 - x + x - 7 - 1 - x = 9

x^{2} - 1 = x^{2} - 5

x^{3} + 3 x - 2 = 2

What is the answer to x^{2/3}-7x^{1/3}+10=0 ?
The answer to x^{2/3}-7x^{1/3}+10=0 is x=125,x=8
Solve for x: x^{2/3}-7x^{1/3}+10=0
The solution is x=125,x=8