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Decimal expansion of x < 0 satisfying 3*x^2 + 3*x*cos(x) = 2.
3

%I #10 Aug 03 2021 14:29:56

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

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

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

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

%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.

%e negative: -1.0835116610219289883304749103821255...

%e positive: 0.48645750461686637457544128449375285...

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

%t f[x_] := a*x^2 + b*x*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, -.9}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199293 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .48, .49}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199294 *)

%Y Cf. A199170, A199294.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 05 2011

%E a(90) onwards corrected by _Georg Fischer_, Aug 03 2021