If (√2 + √5 - √3) × k = -12, then what will be the value of k?

Solution (By Examveda Team)

$$\eqalign{ & \left( {\sqrt 2 + \sqrt 5 - \sqrt 3 } \right) \times {\text{k}} = - 12 \cr & {\text{In these type of questions, we can go through option}} \cr & {\text{From option D}} \cr & \Rightarrow \left( {\sqrt 2 + \sqrt 5 - \sqrt 3 } \right)\left( {\sqrt 2 + \sqrt 5 + \sqrt 3 } \right)\left( {2 - \sqrt {10} } \right) = - 12 \cr & \Rightarrow \left[ {{{\left( {\sqrt 2 + \sqrt 5 } \right)}^2} - {{\left( {\sqrt 3 } \right)}^2}} \right]\left( {2 - \sqrt {10} } \right) = - 12 \cr & \Rightarrow \left( {2 + 5 + 2\sqrt {10} - 3} \right)\left( {2 - \sqrt {10} } \right) = - 12 \cr & \Rightarrow 2\left( {2 + \sqrt {10} } \right)\left( {2 - \sqrt {10} } \right) = - 12 \cr & \Rightarrow 2\left[ {{{\left( 2 \right)}^2} - {{\left( {\sqrt {10} } \right)}^2}} \right] = - 12 \cr & \Rightarrow 2 \times \left[ { - 6} \right] = - 12 \cr & \Rightarrow - 12 = - 12\,\,\,\,\left( {{\text{Satisfy}}} \right) \cr} $$