If $$x^4 + x^{-4} = 1154,(x > 0)$$, then the value of $$2(x - 3)^2$$ is:

Given  $$x^4 + \frac{1}{x^4} = 1154$$

$$\Rightarrow x^4 + \frac{1}{x^4} + 2 = 1154 + 2$$

$$\Rightarrow(x^2 + \frac{1}{x^2})^2 = 1156$$

$$\Rightarrow(x^2 + \frac{1}{x^2} )= 34$$

$$\Rightarrow x^2 + \frac{1}{x^2} + 2= 34 + 2$$

$$\Rightarrow (x + \frac{1}{x})^2 = 36$$

$$\Rightarrow x + \frac{1}{x} = 6 $$

$$\Rightarrow \frac{x^2 + 1}{x} = 6$$

$$\Rightarrow x^2 + 1 = 6x$$

$$\Rightarrow x^2 - 6x = -1$$

$$\Rightarrow x^2 - 6x + 9 = -1 + 9$$

$$\Rightarrow (x - 3)^2 = 8 $$

$$\Rightarrow 2(x - 3)^2 = 2*8 \Rightarrow16$$