X^3+1/x^3=216 and find the value of x+1/x
 

Asked by akashkumar2005 | 17th Sep, 2015, 03:55: PM

Expert Answer:

G i v e n space t h a t space x cubed plus 1 over x cubed equals 216 W E space k n o w space t h a t comma open parentheses a plus b close parentheses cubed equals a cubed plus b cubed plus 3 a b open parentheses a plus b close parentheses T h u s comma space open parentheses x plus 1 over x close parentheses cubed equals x cubed plus 1 over x cubed plus 3 x cross times 1 over x cross times open parentheses x plus 1 over x close parentheses space space space space space space space space space space space space space space equals x cubed plus 1 over x cubed plus 3 cross times open parentheses x plus 1 over x close parentheses space space space space space space space space space space space space space space equals 216 plus 3 open parentheses x plus 1 over x close parentheses S u b s t i t u t i n g space equals y comma space w e space h a v e comma y cubed equals 216 plus 3 y rightwards double arrow y cubed minus 3 y minus 216 equals 0 rightwards double arrow y almost equal to 6.13 rightwards double arrow x plus 1 over x almost equal to 6.13 space space space space space space space space

Answered by Vimala Ramamurthy | 18th Sep, 2015, 09:20: AM