What is the answer to x^3+4x-2=sqrt(2x) ?

The answer to x^3+4x-2=sqrt(2x) is x\approx 0.70865…

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x^3+4x-2=sqrt(2x)

x^{3} + 4 x - 2 = 2 x

x \approx 0.70865 \dots

Solution steps

x^{3} + 4 x - 2 = 2 x

Square both sides:

x^{6} + 8 x^{4} - 4 x^{3} + 16 x^{2} - 16 x + 4 = 2 x

x^{6} + 8 x^{4} - 4 x^{3} + 16 x^{2} - 16 x + 4 = 2 x

Solve

x^{6} + 8 x^{4} - 4 x^{3} + 16 x^{2} - 16 x + 4 = 2 x : x \approx 0.29971 \dots, x \approx 0.70865 \dots

x \approx 0.29971 \dots, x \approx 0.70865 \dots

Verify Solutions:

x \approx 0.29971 \dots

False

, x \approx 0.70865 \dots

True

The solution is

x \approx 0.70865 \dots

5 = 3 + 4 x^{- \frac{1}{6}}

2 = - x + 3

3 a - 5 = a - 3

x = 4 x

What is the answer to x^3+4x-2=sqrt(2x) ?
The answer to x^3+4x-2=sqrt(2x) is x\approx 0.70865…
Solve for x: x^3+4x-2=sqrt(2x)
The solution is x\approx 0.70865…