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

%I #6 Feb 07 2025 16:44:04

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

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

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

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

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

%e least x: -1.303688236082731236157942349201731581...

%e greatest x: 0.68722829225254885401536676699761905...

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

%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, -1.31, -1.30}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198126 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198127 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 22 2011