Question
Sun March 15, 2015 By: Ravi Consul

Q:Prove that
Q:Prove that
 where  are in A, Question no 89312, Mathematics are in A.P.

Expert Reply
Rohit Ranawat
Mon March 16, 2015
W e space k n o w space t h a t comma space alpha comma space beta space a n d space gamma space a r e space i n space A. P beta minus alpha equals gamma minus beta 2 beta equals space a plus gamma..... left parenthesis 1 right parenthesis open square brackets table row cell x minus 3 end cell cell x minus 4 end cell cell x minus alpha end cell row cell x minus 2 end cell cell x minus 3 end cell cell x minus beta end cell row cell x minus 1 end cell cell x minus 2 end cell cell x minus gamma end cell end table close square brackets equals space left parenthesis x minus 3 right parenthesis left square bracket left parenthesis x minus 3 right parenthesis left parenthesis x minus gamma right parenthesis minus left parenthesis x minus 2 right parenthesis left parenthesis x minus beta right parenthesis right square bracket space space minus space left parenthesis x minus 4 right parenthesis left square bracket left parenthesis x minus 2 right parenthesis left parenthesis x minus gamma right parenthesis space minus space left parenthesis x minus 1 right parenthesis left parenthesis x minus gamma right parenthesis right square bracket space plus left parenthesis x minus alpha right parenthesis left square bracket left parenthesis x minus 2 right parenthesis squared space minus space left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis right square bracket equals space left parenthesis x minus 3 right parenthesis left square bracket left parenthesis x squared minus 3 x plus 3 gamma minus x gamma right parenthesis space minus space left parenthesis x squared minus beta x minus 2 x plus 2 beta right parenthesis right square bracket space minus left parenthesis x minus 4 right parenthesis left square bracket left parenthesis x squared minus x gamma minus 2 x plus 2 gamma right parenthesis space minus space left parenthesis x squared minus x beta minus x plus beta right parenthesis space plus left parenthesis x minus alpha right parenthesis left square bracket left parenthesis x squared minus 4 x plus 4 right parenthesis minus left parenthesis x squared minus 4 x plus 3 right parenthesis right square bracket equals space 3 x squared plus 3 x minus x squared gamma plus beta x squared plus 2 x squared minus 2 beta x plus 9 x minus 9 gamma plus 3 x gamma minus 3 beta x plus x y squared plus x squared minus 2 x gamma minus x squared beta plus x beta minus 4 x gamma minus 4 x plus 8 gamma plus 4 x beta minus 4 beta plus x minus alpha equals space 2 beta minus a minus y equals space alpha plus gamma minus a minus y space space space left square bracket f r o m left parenthesis 1 right parenthesis right square bracket equals space 0
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