%I #5 Mar 30 2012 18:57:53

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

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

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

%N Decimal expansion of x>0 having x^2+x=3*cos(x).

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

%e negative: -1.389437452704828389291498251429189255963...

%e positive: 0.9297344303618125096887004946976108824038...

%t a = 1; b = 1; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -2, 1.5}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197811 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197812 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 20 2011