x squared plus 1 over x squared equals 14 comma space f i n d space t h e space space x cubed plus 1 over x cubed space

Asked by kishor.kp14 | 19th Jun, 2019, 09:44: AM

Expert Answer:

begin mathsize 16px style We space know space that comma
open parentheses straight x space plus space 1 over straight x close parentheses squared space equals straight x squared space plus space 1 over straight x squared space plus 2
rightwards double arrow space open parentheses straight x space plus space 1 over straight x close parentheses squared space equals 14 space plus 2 space space space space space space space space space space space space space space..... space space space since space straight x squared space plus space 1 over straight x squared space equals space 14 space
rightwards double arrow space open parentheses straight x space plus space 1 over straight x close parentheses squared space equals 16 space
Taking space square space root space on space both space the space sides comma space we space get
rightwards double arrow space straight x space plus space 1 over straight x space equals space plus-or-minus 4
We space know space that comma
straight x cubed space plus space 1 over straight x cubed space equals space open parentheses straight x space plus space 1 over straight x close parentheses open parentheses straight x squared space plus space 1 over straight x squared space minus space 1 close parentheses equals space plus-or-minus 4 open parentheses 14 space minus space 1 close parentheses space equals space plus-or-minus 4 cross times space 13
rightwards double arrow straight x cubed space plus space 1 over straight x cubed space equals space 4 space cross times space 13 space equals space 52 space space or space straight x cubed space plus space 1 over straight x cubed space equals space minus 4 space cross times space 13 space equals space minus 52 end style

Answered by Yasmeen Khan | 19th Jun, 2019, 10:03: AM