I f space space space open vertical bar table row a b cell space space space a x plus b y end cell row b c cell space space space b x plus c y end cell row cell z minus y space end cell cell space space x minus y end cell 0 end table close vertical bar space space space equals space 0 space comma space t h e n space p r o v e space t h a t space a comma b comma c space a r e space i n space G. P. space O R space x comma y comma z space a r e space i n space G. P. space space left square bracket space W I T H space E X P L A N A T I O N right square bracket

Asked by yash.bisht9910 | 12th Jun, 2015, 01:07: PM

Expert Answer:

E x p a n d i n g space t h e space d e t e r m i n a n t comma space w e space g e t space fraction numerator 1 over denominator x y end fraction open square brackets b y open parentheses b x plus c y close parentheses open parentheses z x minus y squared close parentheses minus c y open parentheses a x plus b y close parentheses open parentheses z x minus y squared close parentheses close square brackets equals 0 rightwards double arrow fraction numerator 1 over denominator x y end fraction open parentheses z x minus y squared close parentheses y open square brackets b open parentheses b x plus c y close parentheses minus c open parentheses a x plus b y close parentheses close square brackets equals 0 rightwards double arrow fraction numerator 1 over denominator x y end fraction open parentheses z x minus y squared close parentheses y open square brackets b squared x minus a c x close square brackets equals 0 rightwards double arrow fraction numerator 1 over denominator x y end fraction x y open parentheses z x minus y squared close parentheses open parentheses b squared minus a c close parentheses equals 0 rightwards double arrow open parentheses z x minus y squared close parentheses open parentheses b squared minus a c close parentheses equals 0 rightwards double arrow z x equals y squared space o r space a c equals b squared rightwards double arrow e i t h e r space x comma y comma z space a r e space i n space G. P. space o r space a comma b comma c space a r e space i n space G. P. space left parenthesis P r o v e d. right parenthesis

Answered by satyajit samal | 14th Jun, 2015, 08:04: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.