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A199278 Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=3.

%I A199278 #8 Feb 07 2025 16:44:05
%S A199278 8,1,3,4,7,5,0,2,3,5,5,4,2,9,3,5,5,1,0,8,9,8,9,9,3,4,1,1,6,9,3,0,4,5,
%T A199278 9,9,8,5,1,3,2,2,5,1,0,7,6,4,4,5,2,9,3,6,4,0,3,3,1,6,7,2,4,5,3,7,1,2,
%U A199278 1,6,3,1,0,6,1,9,5,6,3,7,8,8,5,9,1,7,3,2,4,5,3,5,4,6,6,1,7,5,5
%N A199278 Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=3.
%C A199278 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199278 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199278 negative: -1.3773686718388251570629963805293335...
%e A199278 positive:  0.8134750235542935510898993411693045...
%t A199278 a = 2; b = 3; c = 3;
%t A199278 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199278 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199278 r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
%t A199278 RealDigits[r]    (* A199277 *)
%t A199278 r = x /. FindRoot[f[x] == g[x], {x, .81, .82}, WorkingPrecision -> 110]
%t A199278 RealDigits[r]   (* A199278 *)
%Y A199278 Cf. A199170.
%K A199278 nonn,cons
%O A199278 0,1
%A A199278 _Clark Kimberling_, Nov 04 2011