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%I #7 Aug 09 2021 07:44:20
%S 5,8,0,4,5,7,1,2,4,4,4,5,9,3,3,1,6,1,7,9,7,2,1,9,6,5,1,4,2,8,8,1,9,0,
%T 7,5,8,9,3,8,9,8,1,1,3,7,0,7,3,9,1,2,4,9,1,2,2,4,0,8,6,1,6,7,8,2,2,5,
%U 7,9,9,5,6,9,8,9,0,1,5,7,4,9,9,8,9,7,4,5,1,3,3,1,9,1,6,1,8,0,9,6,6,5
%N Decimal expansion of greatest x having 4*x^2+2x=3*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -0.95434777660875567212090095479339137329...
%e greatest x: 0.58045712444593316179721965142881907589...
%t a = 4; b = 2; c = 3;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 1}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198359 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198360 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 24 2011