1.
Show that the roots r,s,tr, s, t of the cubic x(x−2)(3x−7)=2x(x-2)(3x-7) = 2 are real and positive. Also compute the value of tan⁡−1(r)+tan⁡−1(s)+tan⁡−1(t)\tan^{-1}(r) + \tan^{-1}(s) + \tan^{-1}(t).