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Decimal expansion of x>0 satisfying 4*x^2-3*cos(x)=2.
2

%I #5 Mar 30 2012 18:57:56

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

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

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

%N Decimal expansion of x>0 satisfying 4*x^2-3*cos(x)=2.

%C See A198755 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.9633642134825166666059993347899437523613300...

%t a = 4; b = -3; c = 2;

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

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198997 *)

%Y Cf. A198755.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 01 2011