What is the answer to x^3+1=2\sqrt[3]{2x-1} ?

The answer to x^3+1=2\sqrt[3]{2x-1} is x=1,x\approx 0.61803…,x\approx-1.61803…

Solve for x: x^3+1=2\sqrt[3]{2x-1}

The solution is x=1,x\approx 0.61803…,x\approx-1.61803…

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Popular >

x = 1, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

Solution steps

Take both sides of the equation to the power of

3 : x^{9} + 3 x^{6} + 3 x^{3} + 1 = 16 x - 8

x^{9} + 3 x^{6} + 3 x^{3} + 1 = 16 x - 8

Solve

x^{9} + 3 x^{6} + 3 x^{3} + 1 = 16 x - 8 : x = 1, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

x = 1, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

Verify Solutions:

x = 1

True

, x \approx 0.61803 \dots

True

, x \approx - 1.61803 \dots

True

The solutions are

x = 1, x \approx 0.61803 \dots, x \approx - 1.61803 \dots

1 - x + x + 9 = 4

x - 2 + 4 = x

8 x - 2 x + 2 = 7

4 x - 6 = x + 9

x = - 5

What is the answer to x^3+1=2\sqrt[3]{2x-1} ?
The answer to x^3+1=2\sqrt[3]{2x-1} is x=1,x\approx 0.61803…,x\approx-1.61803…
Solve for x: x^3+1=2\sqrt[3]{2x-1}
The solution is x=1,x\approx 0.61803…,x\approx-1.61803…