If X²+1/x²=5 then find the value of x³+1/x³

Asked by Umahari151104 | 15th Jun, 2019, 12:44: PM

Expert Answer:

begin mathsize 16px style To space find colon space straight x cubed space plus space 1 over straight x cubed equals space ?
space straight x cubed space plus space open parentheses 1 over straight x close parentheses cubed space equals space open parentheses straight x space plus space 1 over straight x close parentheses space open parentheses straight x squared space plus space 1 over straight x squared minus space 1 close parentheses space space space space space.... space space since space straight a cubed plus space straight b cubed equals space left parenthesis straight a space plus space straight b right parenthesis open parentheses straight a squared minus ab space plus space straight b squared close parentheses
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 straight x space plus space 1 over straight x close parentheses space open parentheses 5 minus space 1 close parentheses space space space space space space space space.... since space straight x squared space plus space 1 over straight x squared equals space 5
rightwards double arrow straight x cubed space plus space 1 over straight x cubed equals space 4 open parentheses straight x space plus space 1 over straight x close parentheses
Squaring space on space both space the space sides comma space we space get
open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses squared equals space 16 open parentheses straight x space plus space 1 over straight x close parentheses squared
rightwards double arrow open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses squared equals space 16 open parentheses straight x squared space plus space 1 over straight x squared space plus space 2 space cross times space straight x space cross times space 1 over straight x close parentheses
rightwards double arrow open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses squared equals space 16 open parentheses straight x squared space plus space 1 over straight x squared space plus space 2 space close parentheses space space space
rightwards double arrow open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses squared equals space 16 open parentheses 5 plus space 2 space close parentheses space space space space space space space space.... since space straight x squared space plus space 1 over straight x squared equals space 5
space rightwards double arrow open parentheses straight x cubed space plus space 1 over straight x cubed close parentheses squared equals space 16 space cross times 7
Taking space square space root space on space both space the space sides comma space we space get
straight x cubed space plus space 1 over straight x cubed space equals space 4 square root of 7 space space space space space space space space space end style

Answered by Yasmeen Khan | 15th Jun, 2019, 09:42: PM