If x = x^2 - x + 5/4 , then the value of x will be ?

Answer: Option D

$$\begin{array}{rl}& \cos \pi x=x^2-x+\frac{5}{4}\\ & =x^2-2\times x\times \frac{1}{2}+\frac{1}{4}-\frac{1}{4}+\frac{5}{4}\\ & ={\left(x-\frac{1}{2}\right)}^2+1>1\\ & =-1⩽\cos x⩽1\end{array}$$
∴ So, value of x is none of the above