Question

If m is a root of x² + 3x + 1 = 0, such that the value of tan^-1(m) + tan^-1(1/m) is kπ/2, k ∈ I, then find the value of (k + 4)

Answer 1

Since sum of the roots is negative and product of the roots is positive.

So, both roots are negative

Thus m is a negative root

Now, tan^-1(m) + tan^-1(1/m)

= tan^-1(m) - π + cot^-1(m)

= - π + (tan^-1(m) + cot^-1(m))

= - π + π/2 = - π/2

Clearly, k = -1

Hence, the value of (k + 4) is 3.