What is the answer to 3x^{2/3}-20x^{1/3}-7=0 ?

The answer to 3x^{2/3}-20x^{1/3}-7=0 is x=343,x=-1/27

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3x^{2/3}-20x^{1/3}-7=0

3 x^{\frac{2}{3}} - 20 x^{\frac{1}{3}} - 7 = 0

x = 343, x = - \frac{1}{27}

Decimal

x = 343, x = - 0.03703 \dots

Solution steps

3 x^{\frac{2}{3}} - 20 x^{\frac{1}{3}} - 7 = 0

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

3 (x^{\frac{1}{3}})^{2} - 20 x^{\frac{1}{3}} - 7 = 0

Rewrite the equation with

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

3 u^{2} - 20 u - 7 = 0

Solve

3 u^{2} - 20 u - 7 = 0 : u = 7, u = - \frac{1}{3}

u = 7, u = - \frac{1}{3}

Substitute back

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

solve for

x

Solve

x^{\frac{1}{3}} = 7 : x = 343

Solve

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

x = 343, x = - \frac{1}{27}

Verify Solutions:

x = 343

True

, x = - \frac{1}{27}

True

The solutions are

x = 343, x = - \frac{1}{27}

3 x - 8 = 19

30 - x + 10 = x

x = 4 x + 12

y - 2 6 - y = 3 y - 8

4 3 2 x + 1 = 20

What is the answer to 3x^{2/3}-20x^{1/3}-7=0 ?
The answer to 3x^{2/3}-20x^{1/3}-7=0 is x=343,x=-1/27
Solve for x: 3x^{2/3}-20x^{1/3}-7=0
The solution is x=343,x=-1/27