Question

$show space that open vertical bar table row 1 cell space space space space straight b plus straight c space end cell cell space space space space space straight b squared plus straight c squared end cell row 1 cell space space straight c plus straight a end cell cell space space space straight c squared plus straight a squared end cell row 1 cell space space straight a plus straight b end cell cell space space space space straight a squared plus straight b squared end cell end table close vertical bar$

Solution

Let space increment space equals space open vertical bar table row 1 cell space space space space straight b plus straight c space end cell cell space space space space space straight b squared plus straight c squared end cell row 1 cell space space straight c plus straight a end cell cell space space space straight c squared plus straight a squared end cell row 1 cell space space straight a plus straight b end cell cell space space space space straight a squared plus straight b squared end cell end table close vertical bar space space space space space space space space space space space equals space space open vertical bar table row 1 cell space space space space straight b plus straight c space end cell cell space space space space space straight b squared plus straight c squared end cell row 0 cell space space straight a minus straight b end cell cell space space space space space straight a squared space minus straight b squared end cell row 0 cell space space straight a minus straight c end cell cell space space space space space straight a squared minus straight c squared end cell end table close vertical bar space comma space by space straight R subscript 2 space minus straight R subscript 1 space comma space straight R subscript 3 space minus straight R subscript 1 space space space space space space space space space space equals space left parenthesis straight a minus straight b right parenthesis space left parenthesis straight b minus straight c right parenthesis space space space space space open vertical bar table row 1 cell space space space space straight b plus straight c space end cell cell space space space space space straight b squared plus straight c squared end cell row 0 1 cell space space space space space space straight a plus straight b end cell row 0 1 cell space space space space space space straight a plus straight c end cell end table close vertical bar space space space space space space space space space equals space space left parenthesis straight a minus straight b right parenthesis space left parenthesis straight b minus straight c right parenthesis space space space space open vertical bar table row 1 cell space space space space straight b plus straight c space end cell cell space space space space space straight b squared plus straight c squared end cell row 0 1 cell space space space space space space straight a plus straight b end cell row 0 0 cell space space space space space space space straight c minus straight b end cell end table close vertical bar space comma space by space straight R subscript 3 space minus straight R subscript 2 space space space space space space space space space equals space space left parenthesis straight a minus straight b right parenthesis space left parenthesis straight b minus straight c right parenthesis space open square brackets table row cell left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis space left parenthesis straight c minus straight b right parenthesis end cell end table close square brackets space space space space space space space space space space space equals space left parenthesis straight a minus straight b right parenthesis space left parenthesis straight b minus straight c right parenthesis left parenthesis straight c minus straight b right parenthesis equals left parenthesis straight a minus straight b right parenthesis left parenthesis straight b minus straight c right parenthesis left parenthesis straight c minus straight a right parenthesis

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