If $$\frac{{4\left[ {{{\left( {17} \right)}^3} - {{\left( 7 \right)}^3}} \right]}}{{\left( {{{17}^2} + {7^2} + p} \right)}} = 40,$$     then what is the value of p?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{4\left[ {{{\left( {17} \right)}^3} - {{\left( 7 \right)}^3}} \right]}}{{\left( {{{17}^2} + {7^2} + p} \right)}} = 40 \cr & {\text{We know,}} \cr & \left[ {{a^3} - {b^3} = \left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)} \right] \cr & \frac{{4\left[ {\left( {17 - 7} \right)\left( {{{17}^2} + {7^2} + 17 \times 7} \right)} \right]}}{{{{17}^2} + {7^2} + p}} = 40 \cr & {17^2} + {7^2} + 119 = {17^2} + {7^2} + p \cr & p = 119 \cr} $$