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

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

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

%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=0.42728343876885536400544778356981172491406...

%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, .42, .43}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198994 *)

%Y Cf. A198755.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 01 2011