Question

If m is a root of x² + 3x + 1 = 0, then find the value of tan^-1(m) + tan^-1(1/m).

Answer 1

Let m₁ and m₂ be the roots of

x² + 3x + 1 = 0

Thus, m₁ + m₂ = -3 < 0

and m₁ x m₂ = 1

It is possible only when both are negative.