If a³ + b³ = 218 and a + b = 2, then the value of $$1 - \sqrt {ab} $$  is:

Solution (By Examveda Team)

$$\eqalign{ & {a^3} + {b^3} = 218\,\& \,a + b = 2 \cr & {\left( {a + b} \right)^3} = {\left( 2 \right)^3} \cr & {a^3} + {b^3} + 3\left( {a + b} \right)\left( {ab} \right) = 8 \cr & 218 + 3\left( 2 \right)\left( {ab} \right) = 8 \cr & ab = \frac{{8 - 218}}{6} \cr & ab = \frac{{ - 210}}{6} = - 35 \cr & \sqrt {1 - ab} = \sqrt {1 - \left( { - 35} \right)} \cr & \sqrt {1 - ab} = \sqrt {1 + \left( {35} \right)} \cr & \sqrt {1 - ab} = 6 \cr} $$