If x^2 + x = 5 , then the value of ( x + 3 )^3 + 1 ( x + 3 )^3 = ?

Answer: Option B

$$\begin{array}{rl}& \text{According to the question,}\\ & \Rightarrow {\left(x+3\right)}^3+\frac{1}{{\left(x+3\right)}^3}\\ & \text{Let, }t=x+3,x=t-3\\ & \Rightarrow x^2+x=5\text{, }\left(\text{Given}\right)\\ & \Rightarrow \left(x+1\right)x=5\\ & \Rightarrow \left(t-3+1\right).\left(t-3\right)=5\\ & \Rightarrow \left(t-2\right).\left(t-3\right)=5\\ & \Rightarrow t^2-3t-2t+6=5\\ & \Rightarrow t^2-5t=-1\\ & \Rightarrow t+\frac{1}{t}=5\\ & \Rightarrow {\left(x+3\right)}^3+\frac{1}{{\left(x+3\right)}^3}\\ & \Rightarrow t^3+\frac{1}{t^3}\\ & \Rightarrow {\left(t+\frac{1}{t}\right)}^3-3\times t\times \frac{1}{t}\left(t+\frac{1}{t}\right)\\ & \Rightarrow 5^3-3\times 5\\ & \Rightarrow 125-15\\ & \Rightarrow 110\\ & \therefore {\left(x+3\right)}^3+\frac{1}{{\left(x+3\right)}^3}=110\end{array}$$