Prove that 
begin mathsize 20px style open vertical bar table row cell x plus 1 space space space end cell cell x plus 2 space space space end cell cell x plus alpha end cell row cell x plus 2 space space end cell cell x plus 3 space space end cell cell x plus beta end cell row cell x plus 3 space space end cell cell x plus 4 space space end cell cell x plus gamma end cell end table close vertical bar equals 0 comma w h e r e space alpha comma beta comma gamma space a r e space g i v e n space t o space b e space i n space A. P. end style

Asked by sunil2791 | 22nd Jul, 2017, 09:29: AM

Expert Answer:

begin mathsize 16px style open vertical bar table row cell straight x plus 1 end cell cell straight x plus 2 end cell cell straight x plus straight alpha end cell row cell straight x plus 2 end cell cell straight x plus 3 end cell cell straight x plus straight beta end cell row cell straight x plus 3 end cell cell straight x plus 4 end cell cell straight x plus straight gamma end cell end table close vertical bar
straight R subscript 3 minus straight R subscript 2 comma space straight R subscript 2 minus straight R subscript 1
open vertical bar table row cell straight x plus 1 end cell cell straight x plus 2 end cell cell straight x plus straight alpha end cell row 1 1 cell straight beta minus straight alpha end cell row 1 1 cell straight gamma minus straight beta end cell end table close vertical bar

Here space straight alpha comma straight beta comma straight gamma space are space in space AP
rightwards double arrow straight beta minus straight alpha equals straight gamma minus straight beta
Hence comma space straight R subscript 2 space and space straight R subscript 3 space are space same space determinant space is space 0.
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Answered by Sneha shidid | 22nd Jul, 2017, 10:08: PM