Prove this please I need this..

Asked by 2003.m.harsh | 24th Apr, 2020, 12:29: PM

Expert Answer:

TO prove that: |a,  a+c,  a-b  //  b-c,  b,  b+a  //  c+b,  c-a,  c| = (a+b+c)(a2+b2+c2)
C o n s i d e r comma space
L H S space equals space open vertical bar table row a cell a plus c end cell cell a minus b end cell row cell b minus c end cell b cell b plus a end cell row cell c plus b end cell cell c minus a end cell c end table close vertical bar
M u l t i p l y i n g space R subscript 1 space w i t h space a comma space R subscript 2 space w i t h space b space a n d space R subscript 3 space w i t h space c space r e s p e c t i v e l y comma space w e space h a v e
L H S equals fraction numerator 1 over denominator a b c end fraction open vertical bar table row cell a squared end cell cell a squared plus a c end cell cell a squared minus a b end cell row cell b squared minus b c end cell cell b squared end cell cell b squared plus a b end cell row cell c squared plus b c end cell cell c squared minus a c end cell cell c squared end cell end table close vertical bar
equals fraction numerator 1 over denominator a b c end fraction open vertical bar table row cell a squared plus b squared plus c squared end cell cell a squared plus b squared plus c squared end cell cell a squared plus b squared plus c squared end cell row cell b squared minus b c end cell cell b squared end cell cell b squared plus a b end cell row cell c squared plus b c end cell cell c squared minus a c end cell cell c squared end cell end table close vertical bar space space space space... space A p p l y i n g space R subscript 1 rightwards arrow R subscript 1 plus R subscript 2 plus R subscript 3
equals fraction numerator left parenthesis a squared plus b squared plus c squared right parenthesis over denominator a b c end fraction open vertical bar table row 1 1 1 row cell b squared minus b c end cell cell b squared end cell cell b squared plus a b end cell row cell c squared plus b c end cell cell c squared minus a c end cell cell c squared end cell end table close vertical bar space space space
equals fraction numerator left parenthesis a squared plus b squared plus c squared right parenthesis over denominator a b c end fraction open vertical bar table row 1 0 0 row cell b squared minus b c end cell cell b c end cell cell a b plus b c end cell row cell c squared plus b c end cell cell negative a c minus b c end cell cell negative b c end cell end table close vertical bar
equals fraction numerator b c left parenthesis a squared plus b squared plus c squared right parenthesis over denominator a b c end fraction open vertical bar table row 1 0 0 row cell b minus c end cell c cell a plus c end cell row cell c plus b end cell cell negative a minus b end cell cell negative b end cell end table close vertical bar
equals fraction numerator left parenthesis a squared plus b squared plus c squared right parenthesis over denominator a end fraction open square brackets negative b c plus a squared plus a c plus a b plus b c close square brackets subscript blank
equals fraction numerator left parenthesis a squared plus b squared plus c squared right parenthesis a over denominator a end fraction open square brackets a plus b plus c close square brackets
equals left parenthesis a plus b plus c right parenthesis left parenthesis a squared plus b squared plus c squared right parenthesis

Answered by Renu Varma | 24th Apr, 2020, 06:29: PM