If $x^2 - 3x + 1 = 0,$ then the value of $2(x^8+\frac{1}{x^8})-5(x^2+\frac{1}{x^2})$ is :

4379

We know that,

If $K+\frac{1}{K}=n$

then, $K^2+\frac{1}{K^2}$ = n² – 2

If $x^2 - 3x + 1 = 0,$

then the value of $2(x^8+\frac{1}{x^8})-5(x^2+\frac{1}{x^2})$ = ?

Divide both the sides of If $x^2 - 3x + 1 = 0$ we get,

x + \(\frac{1}{x}\) = 3

then, x² + \(\frac{1}{x^2}\) = 3² – 2 = 7

and, x⁴ + \(\frac{1}{x^4}\) = 7² – 2 = 47

also, x⁸ + \(\frac{1}{x^8}\) = 47² – 2 = 2207

Put these value in desired equation,

2(2207)-5(7) = 4414 - 35 = 4379