Question

$Evaluate space open vertical bar table row 0 cell space space space ab squared end cell cell space space ac squared end cell row cell straight a squared space straight b end cell 0 cell space bc squared end cell row cell straight a squared straight c end cell cell space space straight b squared space straight c end cell cell space 0 end cell end table close vertical bar$

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Solution

Let space space increment space equals space open vertical bar table row 0 cell space space space ab squared end cell cell space space ac squared end cell row cell straight a squared space straight b end cell 0 cell space bc squared end cell row cell straight a squared straight c end cell cell space space straight b squared space straight c end cell cell space 0 end cell end table close vertical bar space equals straight a squared space straight b squared space straight c squared space space open vertical bar table row 0 cell space space space straight a end cell cell space space straight a end cell row straight b cell space space space 0 end cell cell space space space straight b end cell row straight c cell space space space straight c end cell cell space space space 0 end cell end table close vertical bar space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space by space taking space straight a squared comma space straight b squared comma space straight c to the power of 2 space end exponent common space straight C subscript 1 space straight C subscript 2 space straight C subscript 3 space respectively space space space space space equals straight a squared space straight b squared space straight c squared space space open vertical bar table row 0 cell space 0 end cell cell space space straight a end cell row straight b cell space minus straight b space space end cell cell space space straight b end cell row cell straight c space end cell straight c cell space straight c end cell end table close vertical bar space comma space by space straight C subscript 2 space minus straight C subscript 3 space space space space space equals space straight a squared space straight b squared space straight c squared space. straight a space open vertical bar table row straight b cell space space minus straight b end cell row straight c cell space space space space straight c end cell end table close vertical bar space space equals space straight a squared space straight b squared space straight c squared space. straight a space left parenthesis bc plus bc right parenthesis space space space space space equals space straight a squared space straight b squared space straight c squared space. straight a.2 bc space equals space 2 space straight a cubed space straight b cubed space straight c cubed

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