Given m+1/m=5 find m^4+1/m^2/m^2-3m+1=?

• i think its
  
  (m^4+ 1/m^2)/m^2-3m+1
  =(m^4+ 1/m^2)/2m [m+ 1/m=5 => m^2-5m+1=0 => m^2-3m+1=2m ]
  =(1/2)*(m^3 +1/m^3)
  =(1/2)*[(m+ 1/m)^3 -3* m * 1/m *(m+ 1/m)]
  =(1/2)*[5^3 - 3*5]
  =(1/2)*110
  =55
  
• 10 years agoHelpfull: Yes(3) No(1)
• (m+1/m)^2=5^2
  m^2+1/m^2+2=25
  m^2+1/m^2=23
  m^4+1/m^2/m^2-3m+1==>(m^4+1/m^4)-3m+1
  =>(m^2+1/m^2)^2-2-3m+1
  =>(23)^2-2-3m+1
  =>529-2-3m+1
  m=176
• 10 years agoHelpfull: Yes(0) No(0)