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If the square of x minus 3x plus 1 equals 0, then the fourth power of x plus the square of x plus 1 part of x.
X^2-3x+1=0
X-3+1/x=0
X+1/x =3
(X+1/x)^2= x^2+1/x^2+2=9
X^2+1/x^2=7
X^2/(x^4+x^2+1),[ numerator denominator is the same as dividing by x^2]
=1/(X^2+1+1/x^2)
=1/(7+1)
=1/8
The square of x minus 4 plus 1 equals 0 to the fourth power of x plus one-fourth of the fourth power of x The square of x minus 4 plus 1 equals 0 to the fourth power of x plus one of the fourth power of x
X2-4x+1=0 both sides divided by x
X-4+1/x=0
X+1/x =4
Simultaneous square of both sides
X2+2+1/ x2=16
X2+1/ x2=14
Simultaneous square of both sides
X^4+2+1/x^4=196
The fourth power of x plus the fourth power of x =196-2=194
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