x^2-3x+1=0

then

X^5+1/X^5

• x*x=3x-1
  or x=3-1/x
  or x+1/x=3
  
  (x+1/x)^2=9
  x^2+1/X^2=7
  
  (x+1/x)^3=27
  X^3+1/x^3=18
  (x^2+1/x^2)(x^3+1/X^3)=126
  x^5+1/x^5=126-3=132
• 11 years agoHelpfull: Yes(12) No(2)
• x^2-3x-1=0 then we find x
  by quadratic sol.
  (x-2)(x-1)
  x=1,2
  then
  put either 1 or 2 according to the options ans
  by 1
  1^5+1/1^5=2
  by 2
  2^5+1/2^5=32+1/32=32.03125
  
• 11 years agoHelpfull: Yes(3) No(13)
• x^2-3x+1=0 =>x-3+1/x=0 =>x+1/x=3....(i)
  Now, x^5+1/x^5=(x+1/x)(x^4+x^3.1/x+x^2.1/x^2+x.1/x^3+1/x^4)
  putting (i) in here we get,
  3.(x^4+1/x^4+1+1/x^2)
  = 3.[((x+1/x)(x^3+x^2.1/x+x^2.1/x+x.1/x^2+1/x^3)
  =3.3.3(x^2+1/x.x+1/x^2)
  =3.3.3[(x+1/x)^2-2.x.1/x]
  =3.3.3.[3^2-2]
  =27.7
  =189 (ans)
• 10 years agoHelpfull: Yes(0) No(2)