if x+1/x=5 then x^4+3x^3+5x^2+3x+1/x^4+1

• given,
  (x+ 1/x)= 5
  
  (x^2+ 1/x^2) =(x+ 1/x)^2 - 2*x*1/x = 5^2-2 = 23
  
  x^4+3x^3+5x^2+3x+1/x^4+1
  
  dividing Nr & Dr by x^2 we get
  
  (x^2 + 3x + 5 + 3/x + 1/x^2) / (x^2+ 1/x^2)
  
  =[(x^2+ 1/x^2) + 5 + 3(x+ 1/x)] / (x^2+ 1/x^2)
  
  = (23 + 5 + 3*5)/23
  = 43/23
• 10 years agoHelpfull: Yes(8) No(1)
• x + 1/x = 5
  x^2 + 1/x^2 = 5^2 - 2 =23
  
  x^4+3x^3+5x^2+3x+1/x^4+1
  
  Dividing each term by x^2
  
  (x^2 + 3x + 5 + 3/x + 1/x^2) /(x^2 + 1/x^2)
  = (23 + 3*5 +5 )/23
  =43/23
• 10 years agoHelpfull: Yes(4) No(0)
• divide Numerator and denominator by x^2......
  
  tricky one but solved
• 10 years agoHelpfull: Yes(1) No(1)
• as (x+1)/x=5 so x=1/4...
  so put the value of x in the equation and get the result.
• 10 years agoHelpfull: Yes(1) No(2)