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

%I #7 Aug 05 2021 14:29:49

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

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

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

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

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

%e 1.644647274313462717714642325568159246705870...

%t a = 1; b = -4; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.65}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198840 *)

%Y Cf. A198755.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 30 2011

%E Offset corrected by _Georg Fischer_, Aug 05 2021