According to the problem,

I${\omega _1}$ + I${\omega _2}$ = 2I${\omega _0}$

${\omega _0}$ = ${{\left( {{\omega _1} - {\omega _2}} \right)} \over 2}$

${K_i} = {1 \over 2}I\left( {{\omega _1}^2 + {\omega _2}^2} \right)$

${K_f} = {1 \over 4}{\left( {{\omega _1} + {\omega _2}} \right)^2}$

Loss $\Delta K = I\left[ {{{{\omega _1}^2} \over 2} + {{{\omega _2}^2} \over 2} - {{{\omega _1}^2} \over 4} - {{{\omega _2}^2} \over 4} - {{2{\omega _1}{\omega _2}} \over 4}} \right]$

$= I\left[ {{{{\omega _1}^2} \over 4} + {{{\omega _2}^2} \over 4} - {{2{\omega _1}{\omega _2}} \over 4}} \right]$

$= {I \over 4}{\left[ {{\omega _1} - {\omega _2}} \right]^2}$