If $$x+[\frac{1}{(x+7)}]=0$$, then what is the value of $$x-[\frac{1}{(x+7)}]$$ ?

Given : $$x+[\frac{1}{(x+7)}]=0$$ -----------(i)

=> $$\frac{x^2+7x+1}{x+7}=0$$

=> $$x^2+7x+1=0$$

=> $$x=\frac{-7\pm\sqrt{49-4}}{2}$$

=> $$x=\frac{3\sqrt{5}-7}{2}$$ -----------(ii)

From equation (i), => $$\frac{1}{(x+7)}=-x$$ ---------------(iii)

To find : $$x-[\frac{1}{(x+7)}]$$

Substituting values from equations (ii) and (iii), we get :

= $$x-(-x)=2x$$

= $$2\times\frac{3\sqrt5-7}{2}$$

= $$3\sqrt5-7$$

=> Ans - (B)