If x2 – 4x + 1 = 0, then what is the value of x9 + x7 – 194x5 – 194x3?

If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?

If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?

A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2)/(a + b + c)?

If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?

If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?

If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?

Which of the following statement(s) is/are true?

$$\begin{gathered} I. (65)1/6 > (17)1/4 > (12)1/3 \\ II. (17)1/4 > (65)1/6 > (12)1/3 \\ III. (12)1/3 > (17)1/4 > (65)1/6 \end{gathered}$$