Cubic Equation

$x^2 + \dfrac{b^2}{x^2} + 2b = a^2$ $\Rightarrow x^3 +\left( \dfrac{b}{x} \times b \right ) + 2bx = a^2x$ Substitute $x^3=a+1$ and $\dfrac{b}{x}=a-x$ $\Rightarrow (a+1) + (a-x)b + 2bx = a^2x$ $\Rightarrow (a+1)+ab-bx+2bx=a^2x$ $\Rightarrow ab+a+1=x(a^2 - 2b + b)$ $\Rightarrow \boxed {x=\dfrac{(ab + a +1)}{a^2 - b}}$

put a=26 x=3 which means b=69.....only option A satisfies the values...................................................................................................................but i still dont have any idea of the genuine method