(i)Factorise: 27 x cubed minus y squared minus 9 x y minus 1
(ii)Show :x y open square brackets open parentheses x plus y close parentheses open parentheses 1 over x plus 1 over y close parentheses minus 4 close square bracketsequals open parentheses x minus y close parentheses squared
(iii)factorise:x cubed minus 1 over x cubed minus 3 x plus 3 over x

Asked by araima2001 | 14th Sep, 2014, 07:23: AM

Expert Answer:

open parentheses i i close parentheses C o n s i d e r space t h e space e x p r e s s i o n space x y open square brackets open parentheses x plus y close parentheses open parentheses 1 over x plus 1 over y close parentheses minus 4 close square brackets x y open square brackets open parentheses x plus y close parentheses open parentheses 1 over x plus 1 over y close parentheses minus 4 close square brackets equals x y open square brackets 1 plus x over y plus y over x plus 1 minus 4 close square brackets equals x y open square brackets x over y plus y over x minus 2 close square brackets equals x squared plus y squared minus 2 x y equals open parentheses x minus y close parentheses squared equals R. H. S  open parentheses i i i close parentheses F a c t o r i z e space x cubed minus 1 over x cubed minus 3 x plus 3 over x space x cubed minus 1 over x cubed minus 3 x plus 3 over x equals open parentheses x minus 1 over x close parentheses open parentheses x squared plus 1 over x squared plus 1 close parentheses space minus 3 x plus 3 over x space space space space space space space open square brackets sin c e space a cubed minus b cubed equals open parentheses a minus b close parentheses open parentheses a squared plus b squared plus a b close parentheses close square brackets equals open parentheses x minus 1 over x close parentheses open parentheses x squared plus 1 over x squared plus 1 close parentheses space minus 3 open parentheses x minus 1 over x close parentheses space equals open parentheses x minus 1 over x close parentheses open square brackets open parentheses x squared plus 1 over x squared plus 1 close parentheses space minus 3 close square brackets equals equals open parentheses x minus 1 over x close parentheses open parentheses x squared plus 1 over x squared minus 2 close parentheses

Answered by Vimala Ramamurthy | 14th Sep, 2014, 08:53: AM

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