Question

Let cos^-1(x) + cos^-1(2x) + cos^-1(3x) = π if x satisfies the cubic equation ax³ + bx² + cx - 1 = 0, then find the value of (a + b + c + 2).

Answer 1

We have,

cos^-1(x) + cos^-1(2x) + cos^-1(3x) = π

cos^-1(2x) +cos^-1(3x) = π - cos^-1(x)

cos^-1(2x) + cos^-1(3x) = cos^-1(-x)

Thus a = 12, b = 14, c = 0

Hence, the value of (a + b + c + 2) = 28