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Decimal expansion of greatest x having 3*x^2+2x=2*cos(x).
3

%I #6 Feb 07 2025 16:44:05

%S 5,0,0,8,6,6,3,1,0,2,5,3,0,1,1,7,6,9,7,9,0,8,0,2,7,5,4,6,9,4,6,5,6,3,

%T 3,0,3,2,1,5,5,6,9,7,4,9,5,5,9,5,6,2,7,5,7,4,5,2,1,3,3,0,3,1,2,7,4,0,

%U 4,8,0,4,4,3,8,4,7,3,5,1,5,1,5,2,3,9,2,8,1,5,2,3,5,5,3,9,3,0,5

%N Decimal expansion of greatest x having 3*x^2+2x=2*cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e least x: -1.014060582687901072214777706552979973...

%e greatest x: 0.500866310253011769790802754694656330...

%t a = 3; b = 2; c = 2;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -2, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.02, -1.01}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198224 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198225 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 22 2011