What is the answer to x^3+1=2(2x-1)^{1/3} ?

The answer to x^3+1=2(2x-1)^{1/3} is x=1,x\approx 0.61803…,x\approx-1.61803…

Solve for x: x^3+1=2(2x-1)^{1/3}

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

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

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

Solution steps

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

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

t + 1 = t + 10

t + 1 = t + 12

x + 2 + x - 4 = 3

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