Known: x ^ 2-3x + 1 = 0, find: algebraic formula x ^ 2 + 1 / x ^ 2 and x ^ 4 + 1 / x ^ 4 value

1、
x^2+1=3x
Square on both sides
x^4+2x^2+1=9x^2
x^4+1=7x^2
Divide both sides by x ^ 2
x^2+1/x^2=7
2、
x^4+1=7x^2
Square on both sides
x^8+2x^4+1=49x^4
x^8+1=47x^4
Divide both sides by x ^ 4
x^4+1/x^4=7

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