if (x^2+1)/x=5 then find the value of (x^12+1)/x^6

• 12098
  
  (x^2+1)/x=5
  ==>x+1/x=5
  ==>x^2+1/x^2=23(squaring on both sides)
  ==>x^4+1/x^4=527(square on both sides)........(1)
  (1)*x^2=>x^6+1/x^2=527x^2.........(2)
  
  (1)/x^2=>x^2+1/x^6=527/x^2.....(3)
  (1)+(2)==>
  X^6+1/X^6+(x^2+1/x^2)=527(x^2+1/x^2)
  ==>x^6+1/x^6=526*23
  ==>(x^12+1)/x^6=12098
  
  
• 12 years agoHelpfull: Yes(1) No(1)
• 12098
  
  (x^2+1)/x=5
  x+1/x = 5
  x^2+1/x^2 = 5^2-2= 23
  cubing both sides,
  x^6+ 1/x^6 +3*x^2*(1/x^2) *(x^2+1/x^2) = 23^3
  x^6+1/x^6 = 23^3 -3*1*23 = 12167-69
  x^6+1/x^6 = 12098 = (x^12+1)/x^6
• 12 years agoHelpfull: Yes(1) No(0)
• 5
  as x^2/x so
  x^12/x^6=5
• 12 years agoHelpfull: Yes(0) No(1)