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show that : ( x /4 - y /3) ( x2 /16 + xy / 12  + y2 / 9) = x3 / 64  -  y2 /27, hence find the value , if x = 3 , y= -1

Asked by nisha_vini29 14th September 2015, 12:25 AM
Answered by Expert
Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n open parentheses x over 4 minus y over 3 close parentheses open parentheses x squared over 16 plus fraction numerator x y over denominator 12 end fraction plus y squared over 9 close parentheses L e t space x over 4 equals X space a n d space y over 3 equals Y T h u s comma space open parentheses x over 4 minus y over 3 close parentheses open parentheses x squared over 16 plus fraction numerator x y over denominator 12 end fraction plus y squared over 9 close parentheses equals open parentheses X minus Y close parentheses open parentheses X squared plus X Y plus Y squared close parentheses... left parenthesis 1 right parenthesis W e space k n o w space t h a t comma space open parentheses a cubed minus b cubed close parentheses equals open parentheses a minus b close parentheses open parentheses a squared plus a b plus b squared close parentheses T h u s comma space e q u a t i o n space left parenthesis 1 right parenthesis space b e c o m e s comma open parentheses x over 4 minus y over 3 close parentheses open parentheses x squared over 16 plus fraction numerator x y over denominator 12 end fraction plus y squared over 9 close parentheses equals open parentheses X cubed minus Y cubed close parentheses G i v e n space t h a t space x equals 3 comma space y equals negative 1 therefore open parentheses x over 4 minus y over 3 close parentheses open parentheses x squared over 16 plus fraction numerator x y over denominator 12 end fraction plus y squared over 9 close parentheses equals open parentheses x over 4 close parentheses cubed minus open parentheses y over 3 close parentheses cubed space space space space space space space space space space space space space space space space space space space space space space space space 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 open parentheses 3 over 4 close parentheses cubed minus open parentheses fraction numerator negative 1 over denominator 3 end fraction close parentheses cubed space space space space space space space space space space space space space space space space space space space space space space space space 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 27 over 64 plus 1 over 27 space space space space space space space space space space space space space space space space space space space space space space space space 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 fraction numerator 729 plus 64 over denominator 1728 end fraction space space space space space space space space space space space space space space space space space space space space space space space space 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 793 over 1728

Answered by Expert 14th September 2015, 6:02 PM
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