Question

If cos-1x + cos-1(2x) + cos-1(3x) and x satisfies the equation ax3 + bx2 + cx = 1 then find the value of a2 + b2 + c2 + 10.

Answer 1

Given, cos-1x + cos-1(2x) + cos-1(3x) = π

⇒ cos-12x + cos-13x = π - cos-1x

⇒ cos-12x + cos-13x = cos-1(-x)

Also, ax3 + bx2 + cx = 1

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

Hence, the value of a2 + b2 + c2 + 10

= 144 + 196 + 10

= 350