What is the answer to x^3-9x^{2/3}+8=0 ?

The answer to x^3-9x^{2/3}+8=0 is x=1,x\approx-0.76791…,x\approx 1.67327…

Solve for x: x^3-9x^{2/3}+8=0

The solution is x=1,x\approx-0.76791…,x\approx 1.67327…

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x^{3} - 9 x^{\frac{2}{3}} + 8 = 0

x = 1, x \approx - 0.76791 \dots, x \approx 1.67327 \dots

Solution steps

x^{3} - 9 x^{\frac{2}{3}} + 8 = 0

Remove roots

- 729 x^{2} = - x^{9} - 24 x^{6} - 192 x^{3} - 512

Solve

- 729 x^{2} = - x^{9} - 24 x^{6} - 192 x^{3} - 512 : x = 1, x \approx - 0.76791 \dots, x \approx 1.67327 \dots

x = 1, x \approx - 0.76791 \dots, x \approx 1.67327 \dots

Verify Solutions:

x = 1

True

, x \approx - 0.76791 \dots

True

, x \approx 1.67327 \dots

True

The solutions are

x = 1, x \approx - 0.76791 \dots, x \approx 1.67327 \dots

A x + B x - C = 0

y, y^{\frac{2}{3}} = x

\frac{x}{4} = 2 x - 15

(- 3 x + 18)^{\frac{1}{2}} = x

x = 3 x + 1

What is the answer to x^3-9x^{2/3}+8=0 ?
The answer to x^3-9x^{2/3}+8=0 is x=1,x\approx-0.76791…,x\approx 1.67327…
Solve for x: x^3-9x^{2/3}+8=0
The solution is x=1,x\approx-0.76791…,x\approx 1.67327…