If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

If α and β are the roots of equation x2 – x + 1 = 0, then which equation will have roots α3 and β3?

If x1x2x3 = 4(4 + x1 + x2 + x3 ), then what is the value of [1/(2 + x1 )] + [1/(2 + x2 )] + [1/(2 + x3 )]?

If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3 – 3PQR?

If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?

x, y and z are real numbers. If x3 + y3 + z3 = 13, x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?

If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?

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