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CBSE Class 11-science Answered

log subscript e superscript a space end superscript divided by y minus z equals log subscript e space end subscript superscript b divided by z minus x equals log subscript e superscript c divided by x minus y space space space space space space space space space space. space T h e n space p r o v e left parenthesis space a to the power of y 2 plus y z plus z 2 end exponent right parenthesis. left parenthesis b to the power of z 2 plus x z plus x 2 end exponent right parenthesis. left parenthesis c to the power of x 2 plus y 2 plus x y end exponent right parenthesis equals 1
Asked by Moorti | 04 Jul, 2019, 03:55: PM
answered-by-expert Expert Answer
fraction numerator log subscript e space a over denominator y minus z end fraction equals fraction numerator begin display style log subscript e end style begin display style space end style begin display style b end style over denominator z minus x end fraction equals fraction numerator begin display style log subscript e end style begin display style space end style begin display style c end style over denominator x minus y end fraction equals k rightwards double arrow log subscript e space a equals k left parenthesis y minus z right parenthesis comma space space log subscript e space b equals k left parenthesis z minus x right parenthesis space space space a n d space space log subscript e space c equals k left parenthesis x minus y right parenthesis C o n s i d e r comma log left square bracket left parenthesis a to the power of y squared plus y z plus z squared end exponent right parenthesis. left parenthesis b to the power of z squared plus x z plus x squared end exponent right parenthesis. left parenthesis c to the power of x squared plus x y plus y squared end exponent right parenthesis right square bracket equals log subscript e space left parenthesis a to the power of y squared plus y z plus z squared end exponent right parenthesis space plus space log subscript e space left parenthesis b to the power of z squared plus x z plus x squared end exponent right parenthesis space plus space log subscript e space left parenthesis c to the power of x squared plus x y plus y squared end exponent right parenthesis equals left parenthesis y squared plus y z plus z squared right parenthesis space log subscript e space a plus space left parenthesis z squared plus x z plus x squared right parenthesis log subscript e space b plus left parenthesis x squared plus x y plus y squared right parenthesis log subscript e space c equals left parenthesis y squared plus y z plus z squared right parenthesis space k left parenthesis y minus z right parenthesis plus space left parenthesis z squared plus x z plus x squared right parenthesis k left parenthesis z minus x right parenthesis plus left parenthesis x squared plus x y plus y squared right parenthesis space k left parenthesis x minus y right parenthesis equals k left square bracket left parenthesis y cubed minus z cubed right parenthesis plus left parenthesis z cubed minus x cubed right parenthesis plus left parenthesis x cubed minus y cubed right parenthesis equals k left square bracket 0 right square bracket equals 0 rightwards double arrow e to the power of log left square bracket left parenthesis a to the power of y squared plus y z plus z squared end exponent right parenthesis. left parenthesis b to the power of z squared plus x z plus x squared end exponent right parenthesis. left parenthesis c to the power of x squared plus x y plus y squared end exponent right parenthesis right square bracket end exponent equals e to the power of 0 equals 1 rightwards double arrow left parenthesis a to the power of y squared plus y z plus z squared end exponent right parenthesis. left parenthesis b to the power of z squared plus x z plus x squared end exponent right parenthesis. left parenthesis c to the power of x squared plus x y plus y squared end exponent right parenthesis equals 1
Answered by Renu Varma | 05 Jul, 2019, 09:33: AM

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