If $$\cos \pi x = {x^2} - x + \frac{5}{4}{\text{,}}$$     then the value of x will be ?

Solution (By Examveda Team)

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