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75. $Evalute space space open vertical bar table row cell straight b plus straight c end cell straight a straight a row straight b cell space space space space straight c plus straight a end cell straight b row straight c straight c cell space space straight a plus straight b end cell end table close vertical bar$

Let space space increment space equals space space open vertical bar table row cell straight b plus straight c end cell straight a straight a row straight b cell space space space space straight c plus straight a end cell straight b row straight c straight c cell space space straight a plus straight b end cell end table close vertical bar space space space space space space space space space space space space space equals space left parenthesis straight b plus straight c right parenthesis space space open vertical bar table row cell straight c plus straight a end cell cell space space straight b end cell row straight c cell space space straight a plus straight b end cell end table close vertical bar space minus straight a space open vertical bar table row straight b cell space space space space space space space space straight b end cell row straight c cell space space space space space straight a plus straight b end cell end table close vertical bar space plus straight a space open vertical bar table row straight b cell space space space straight c plus straight a end cell row straight c straight c end table close vertical bar space space space space space space space space space space space space space equals space left parenthesis straight b plus straight c right parenthesis space space open square brackets table row cell left parenthesis straight c plus straight a right parenthesis left parenthesis straight a plus straight b right parenthesis minus bc end cell end table close square brackets space minus straight a space open square brackets table row cell straight b left parenthesis straight a plus straight b right parenthesis minus bc end cell end table close square brackets space plus straight a space open square brackets table row cell straight b minus straight c left parenthesis straight c plus straight a right parenthesis end cell end table close square brackets space space space space space space space space space space space space equals space left parenthesis straight b plus straight c right parenthesis space left parenthesis ca plus straight a squared space plus ab right parenthesis minus straight a left parenthesis ab plus straight b squared space minus bc right parenthesis space plus straight a space left parenthesis bc minus straight c squared space minus ca right parenthesis space space space space space space space space space space space space equals space abc plus straight a squared space straight b plus ab squared space plus straight c squared space straight a plus straight c space straight a to the power of 2 space end exponent space plus abc plus abc minus ac squared space minus ca squared space space space space space space space space space space space space equals space 4 abc

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76.

show that
$open vertical bar table row 1 cell space space space space straight x end cell cell space space space space straight x squared end cell row cell straight x squared end cell cell space space 1 end cell cell space space straight x end cell row straight x cell space space straight x squared end cell cell space space 1 end cell end table close vertical bar space equals space left parenthesis 1 minus x cubed right parenthesis squared$

70 Views

77.

Using space properties space of space determinants comma space prove space that space open vertical bar table row cell straight y plus straight z end cell cell space space space straight x end cell cell space space straight y end cell row cell straight z plus straight x end cell cell space space straight z end cell cell space space straight x end cell row cell straight x plus straight y end cell cell space space straight y end cell cell space straight z end cell end table close vertical bar space equals space left parenthesis straight x plus straight y plus straight z right parenthesis space left parenthesis straight x minus straight z right parenthesis squared

73 Views

78.

Using space properties space of space determinants comma space prove space that open vertical bar table row cell straight y plus straight z end cell straight z cell space space straight y end cell row straight z cell space space straight z plus straight x end cell cell space space straight x end cell row straight y straight x cell space space space straight x plus straight y end cell end table close vertical bar space equals 4 xyz

66 Views

79.

show space that open vertical bar table row straight a cell space space space space space space space space space straight a plus straight b end cell cell straight a plus straight b plus straight c end cell row cell 2 straight a end cell cell space space space space space space space space 3 straight a plus 2 straight b end cell cell space space 4 straight a plus 3 straight b plus 2 straight c end cell row cell 3 straight a end cell cell space space space space space 6 straight a plus straight b end cell cell space space space space space 10 straight a plus 6 straight b plus 3 straight c end cell end table close vertical bar space equals straight a cubed

98 Views

80.

Show that $open vertical bar table row cell straight a plus straight b plus 2 straight c end cell straight a straight b row straight c cell space space space space space straight b plus straight c plus 2 straight a end cell straight b row straight c straight a cell space space straight c plus straight a plus 2 straight b end cell end table close vertical bar$

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