Solve $\sqrt{x^2+1}-\sqrt{4x^4-4x^2+2}=2x^3-x-1$

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Could you please help me solve for $x$ in $$\sqrt{x^2+1}-\sqrt{4x^4-4x^2+2}=2x^3-x-1.$$


I tried this way. But I could not solve further. Please help me.

$$(\sqrt{x^2+1}-\sqrt{4x^4-4x^2+2})^2=(2x^3-x-1)^2$$