Determine the value of 'x', if $$x = \frac{{{{\left( {943 + 864} \right)}^2} - {{\left( {943 - 864} \right)}^2}}}{{\left( {1886 \times 1728} \right)}}$$

Solution (By Examveda Team)

$$\eqalign{ & a = 943\,\,\therefore 2a = 1886 \cr & b = 864\,\,\therefore 2b = 1728 \cr & \therefore {\text{Expression}} \cr & = \frac{{{{\left( {a + b} \right)}^2} - {{\left( {a - b} \right)}^2}}}{{2a \times 2b}} \cr & = \frac{{4ab}}{{4ab}} \cr & = 1 \cr} $$