Given x ^ 2-3x + 1 = 0, find the value of algebraic formula x ^ 4 + 1 / x ^ 4 Such as the title

Given x ^ 2-3x + 1 = 0, find the value of algebraic formula x ^ 4 + 1 / x ^ 4 Such as the title

x²+1=3x
Square on both sides
x^4+2x²+1=9x²
x^4+1=7x²
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=47