If 9x^2 - 6x + 1= 0, then the value of 27x^3 + (27x^3)^-1 will be :

If $9x^2 - 6x + 1= 0,$

then the value of $27x^3 + (27x^3)^{-1}$ = ?

Divide the equation by 3x on both the sides, we get

3x + \(\frac{1}{3x}\) = 2

Now we know that,

If x + \(\frac{1}{x}\)  = n

then, $x^3 +\frac{1}{x^3}$ = n³ - 3 × n

So, $27x^3 + (27x^3)^{-1}$ = 2³ - 3 × 2 = 8 - 6 = 2