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  4. If x1, x2 are roots of the equation x2-6 x+4=0, then find the value of ((x1-2)16+(x2-6)8/x18).

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Q. If $x_1, x_2$ are roots of the equation $x^2-6 x+4=0$, then find the value of $\frac{\left(x_1-2\right)^{16}+\left(x_2-6\right)^8}{x_1^8}$.

Complex Numbers and Quadratic Equations

Solution:

Expression $=\frac{256 x_1^8+\frac{4^8}{x_2^8}}{x_1^8}=256+1=257$