Question
Sat April 18, 2015 By: Kriti Bajpai

If 2(x^2+1)=5x then find:
 
1) x-1/x
2)x^3-1/x^3

Expert Reply
Vimala Ramamurthy
Sun April 19, 2015
C o n s i d e r space t h e space g i v e n space e q u a t i o n space 2 open parentheses x squared plus 1 close parentheses equals 5 x rightwards double arrow fraction numerator open parentheses x squared plus 1 close parentheses over denominator x end fraction equals 5 over 2 rightwards double arrow open parentheses x plus 1 over x close parentheses equals 5 over 2 rightwards double arrow open parentheses x plus 1 over x close parentheses squared equals open parentheses 5 over 2 close parentheses squared rightwards double arrow x squared plus 1 over x squared plus 2 equals 25 over 4 rightwards double arrow x squared plus 1 over x squared equals 25 over 4 minus 2 rightwards double arrow x squared plus 1 over x squared minus 2 equals 25 over 4 minus 2 minus 2 rightwards double arrow x squared plus 1 over x squared minus 2 equals 25 over 4 minus 4 rightwards double arrow open parentheses x minus 1 over x close parentheses squared equals fraction numerator 25 minus 16 over denominator 4 end fraction rightwards double arrow open parentheses x minus 1 over x close parentheses squared equals 9 over 4 rightwards double arrow open parentheses x minus 1 over x close parentheses squared equals open parentheses 3 over 2 close parentheses squared rightwards double arrow x minus 1 over x equals 3 over 2  W e space k n o w space t h a t comma space a cubed minus b cubed 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 x cubed minus 1 over x cubed equals open parentheses x minus 1 over x close parentheses open parentheses x squared plus 1 plus 1 over x squared close parentheses rightwards double arrow space x cubed minus 1 over x cubed equals open parentheses x minus 1 over x close parentheses open parentheses 25 over 4 minus 2 plus 1 close parentheses space space space space open square brackets because x squared plus 1 over x squared equals 25 over 4 minus 2 close square brackets rightwards double arrow space x cubed minus 1 over x cubed equals open parentheses 3 over 2 close parentheses open parentheses 25 over 4 minus 2 plus 1 close parentheses rightwards double arrow space x cubed minus 1 over x cubed equals open parentheses 3 over 2 close parentheses open parentheses 25 over 4 minus 1 close parentheses rightwards double arrow space x cubed minus 1 over x cubed equals open parentheses 3 over 2 close parentheses open parentheses fraction numerator 25 minus 4 over denominator 4 end fraction close parentheses rightwards double arrow space x cubed minus 1 over x cubed equals open parentheses 3 over 2 close parentheses open parentheses 21 over 4 close parentheses rightwards double arrow space x cubed minus 1 over x cubed equals 63 over 8
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