If the sum of two numbers is 3 and the sum of their squares is 12, then their product is equal to -

$$\eqalign{ & {\text{a + b = 3 }}.......{\text{ (i)}} \cr & {\text{(a and b are two numbers)}} \cr & {{\text{a}}^2}{\text{ + }}{{\text{b}}^2} = 12 \cr & {\text{On squaring}}\,\,{\text{equation (i)}} \cr & {\left( {{\text{a + b}}} \right)^2} = \,{3^2} \cr & {{\text{a}}^2}{\text{ + }}{{\text{b}}^2} + 2{\text{ab}} = 9 \cr & 12 + 2{\text{ab = 9}} \cr & {\text{2ab = - 3}} \cr & {\text{ab = }}-\frac{{3}}{2} \cr} $$