$23$is split into two parts such that the difference between square of each part is equal to $23$. The two parts are

Four of the five parts numbered $\left(1\right), \left(2\right), \left(3\right), \left(4\right)$ and $\left(5\right)$are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.

$$\begin{gathered} (2\mathrm{x}+\mathrm{y})(\mathrm{x}-2\mathrm{y})=2\mathrm{x}(\mathrm{x}-3\mathrm{y})+\mathrm{y}(3\mathrm{x}-2\mathrm{y})=2\left({\mathrm{x}}^2-\mathrm{xy}-{\mathrm{y}}^2\right)-\mathrm{xy}=2(\mathrm{x}-\mathrm{y}{)}^2-\mathrm{xy}=2\mathrm{x}(\mathrm{x}-4\mathrm{y})+\mathrm{y}(5\mathrm{x}-2\mathrm{y}) \\ \left(1\right) \left(2\right) \left(3\right) \left(4\right) \left(5\right) \end{gathered}$$

Which of the following values of$\text{'}\mathrm{x}\text{'}$ satisfies the following inequality?

$-12{\mathrm{x}}^2+\mathrm{x}+1>0$