prove that
open parentheses x to the power of b over x to the power of c close parentheses to the power of b plus c minus a end exponent cross times open parentheses x to the power of c over x to the power of a close parentheses to the power of c plus a minus b end exponent cross times open parentheses x to the power of a over x to the power of b close parentheses to the power of a plus b minus c end exponent equals 1

Asked by Neeru | 1st May, 2016, 01:29: PM

Expert Answer:

begin mathsize 16px style C o n s i d e r space l e f t space h a n d space s i d e space o f space t h e space g i v e n space e x p r e s s i o n colon
open parentheses x to the power of b over x to the power of c close parentheses to the power of b plus c minus a end exponent cross times open parentheses x to the power of c over x to the power of a close parentheses to the power of c plus a minus b end exponent cross times open parentheses x to the power of a over x to the power of b close parentheses to the power of a plus b minus c end exponent equals x to the power of b open parentheses b plus c minus a close parentheses end exponent over x to the power of c open parentheses b plus c minus a close parentheses end exponent cross times x to the power of c open parentheses c plus a minus b close parentheses end exponent over x to the power of a open parentheses c plus a minus b close parentheses end exponent cross times x to the power of a open parentheses a plus b minus c close parentheses end exponent over x to the power of b open parentheses a plus b minus c 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 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 space space space space space equals x to the power of b open parentheses b plus c minus a close parentheses minus b open parentheses a plus b minus c close parentheses end exponent cross times x to the power of c open parentheses c plus a minus b close parentheses minus c open parentheses b plus c minus a close parentheses end exponent cross times x to the power of a open parentheses a plus b minus c close parentheses minus a open parentheses c plus a minus b 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 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 space space space space space equals x to the power of b open parentheses b plus c minus a minus a minus b plus c close parentheses end exponent cross times x to the power of c open parentheses c plus a minus b minus b minus c plus a close parentheses end exponent cross times x to the power of a open parentheses a plus b minus c minus c minus a plus b close parentheses end exponent
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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 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 space space space space space equals x to the power of open parentheses 2 b c minus 2 a b close parentheses end exponent cross times x to the power of open parentheses 2 a c minus 2 b c close parentheses end exponent cross times x to the power of open parentheses 2 a b minus 2 a c 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 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 space space space space space equals x to the power of open parentheses 2 b c minus 2 a b plus 2 a c minus 2 b c plus 2 a b minus 2 a c 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 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 space space space space space equals x to the power of 0
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 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 space space space space space equals 1
T h u s comma space L. H. S space equals space R. H. S
H e n c e space p r o v e d. end style

Answered by Vimala | 2nd May, 2016, 09:05: AM