S h o w space t h a t space space left parenthesis x to the power of a minus b end exponent right parenthesis to the power of a plus b end exponent space. left parenthesis x to the power of b minus c end exponent right parenthesis to the power of b plus c end exponent space. left parenthesis x to the power of c minus a end exponent right parenthesis to the power of c plus a end exponent equals 1

Asked by kishor.kp14 | 21st Jun, 2019, 02:02: PM

Expert Answer:

begin mathsize 16px style open parentheses straight x to the power of straight a space minus straight b end exponent close parentheses to the power of straight a space plus space straight b end exponent. open parentheses straight x to the power of straight b space minus space straight c end exponent close parentheses to the power of straight b space plus space straight c end exponent. space open parentheses straight x to the power of straight c space minus space straight a end exponent close parentheses to the power of straight c space plus space straight a end exponent space equals space 1
straight L. straight H. straight S space equals space straight x to the power of open parentheses straight a space minus space straight b close parentheses open parentheses straight a space plus space straight b close parentheses end exponent. space straight x to the power of left parenthesis straight b space minus space straight c right parenthesis open parentheses straight b space plus space straight c close parentheses end exponent. space straight x to the power of left parenthesis straight c space minus space straight a right parenthesis open parentheses straight c space plus space straight a close parentheses space end exponent space space space.... space since space open parentheses straight x to the power of straight m close parentheses to the power of straight n space equals space straight x to the power of mn
space space space space space space space space space space equals space straight x to the power of open parentheses straight a squared space minus space straight b squared close parentheses end exponent. space straight x to the power of open parentheses straight b squared space minus space straight c squared close parentheses end exponent space. straight x to the power of open parentheses straight c squared space minus space straight a squared close parentheses end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space...... space since space left parenthesis straight m space minus space straight n right parenthesis left parenthesis straight m space plus space straight n right parenthesis space equals space straight m squared space minus space straight n squared space space space space space space space space space
space space space space space space space space space space equals straight x to the power of open parentheses straight a squared space minus space straight b squared plus straight b squared space minus space straight c squared space close parentheses end exponent. straight x to the power of open parentheses straight c squared space minus space straight a squared close parentheses end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space... space since space straight x to the power of straight m cross times straight x to the power of straight n space space equals space straight x space to the power of straight m plus straight n end exponent
space space space space space space space space space space equals straight x to the power of open parentheses straight a squared space minus space straight b squared plus straight b squared space minus space straight c squared plus straight c squared space minus space straight a squared space space close parentheses end exponent
space space space space space space space space space space equals straight x to the power of 0
space space space space space space space space space space equals space 1
space space space space space space space space space space equals space straight R. straight H. straight S
Hence space proved.
space space space space space space end style

Answered by Yasmeen Khan | 21st Jun, 2019, 04:30: PM