If x+1/x=3 what is the value of x^5 + 1/x^5?

• 
  given that
  x+1/x= 3
  now let us consider
  x^2+1/(x^2)= 9-2=7
  x^4+1/x^4 = 49-2=47
  x*3+1/x^3 = 27-3*1*3=18
  
  (x^4+1/x^4)*(x+1/x) = 47*3= 141
  x^5+1/x^5 + x^3 +1/x^3 = 141
  x^5+1/x^5 = 141-18=123
• 12 years agoHelpfull: Yes(22) No(11)
• x+1/x= 3
  x^2+1/(x^2)= 9-2=7
  x^4+1/x^4 = 49-2=47
  x*3+1/x^3 = 27-3*1*3=18
  
  (x^4+1/x^4)*(x+1/x) = 47*3= 141
  x^5+1/x^5 + x^3 +1/x^3 = 141
  x^5+1/x^5 = 141-18=123
  
  
• 12 years agoHelpfull: Yes(12) No(4)
• If x+1/x=p => x^5 + 1/x^5 = p^5-5*p^3 + 5*p
  put P=3
• 12 years agoHelpfull: Yes(9) No(5)
• 123 is the solution.solving quadratic equation x+1/x=3 we get x=.3819 or 2.618.
• 12 years agoHelpfull: Yes(6) No(11)
• x+1/x= 3
  x^2+1/(x^2)= 9-2=7
  x^4+1/x^4 = 49-2=47
  x*3+1/x^3 = 27-3*1*3=18
  (x^4+1/x^4)*(x+1/x) = 47*3= 141
  x^5+1/x^5 + x^3 +1/x^3 = 141
  x^5+1/x^5 = 141-18=123
• 10 years agoHelpfull: Yes(3) No(1)
• x+1/x=6
  
  (x+1/x)^3=6^3
  x^3+1/x^3+3x+3/x=216
  x^3+1/x^3+3(x+1/x)=216
  (x^3+1/x^3)=6^3-3*6=198
  
  (x^+1/x)^5=6^5
  x^5+1/x^5+(5x^3+5/x^3)+(10x+10/x)
  =7776
  x^5+1/x^5=7776-10*6-198*5
  =6726
• 6 years agoHelpfull: Yes(0) No(0)