If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then $${{a + b} \over {a - b}}$$ is equal to :

For any three positive real numbers a, b and c,

9(25$${a^2}$$ + b²) + 25(c² - 3$$a$$c) = 15b(3$$a$$ + c).
Then

If   A > 0, B > 0   and    A + B = $${\pi \over 6}$$,

then the minimum value of tanA + tanB is :

Let z = 1 + ai be a complex number, a > 0, such that z³ is a real number.

Then the sum 1 + z + z² + . . . . .+ z¹¹ is equal to :