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A199272 Decimal expansion of x>0 satisfying 2*x^2+2*x*cos(x)=3.

%I A199272 #8 Feb 07 2025 16:44:05
%S A199272 9,7,6,3,1,2,2,7,3,6,1,5,1,3,0,1,2,3,0,7,6,4,7,0,1,4,1,3,3,5,0,9,1,5,
%T A199272 6,7,9,6,7,9,5,3,4,3,8,0,9,3,0,7,2,6,9,5,0,4,9,1,0,7,1,7,6,4,3,2,7,7,
%U A199272 0,7,7,1,5,4,3,2,7,9,7,2,8,5,0,0,3,9,9,2,7,6,7,2,6,5,1,8,8,3,9
%N A199272 Decimal expansion of x>0 satisfying 2*x^2+2*x*cos(x)=3.
%C A199272 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199272 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199272 negative: -1.342905122329356157795629258382825825170...
%e A199272 positive:  0.976312273615130123076470141335091567967...
%t A199272 a = 2; b = 2; c = 3;
%t A199272 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199272 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199272 r = x /. FindRoot[f[x] == g[x], {x, -1.35, -1.34}, WorkingPrecision -> 110]
%t A199272 RealDigits[r]   (* A199271 *)
%t A199272 r = x /. FindRoot[f[x] == g[x], {x, .97, .98}, WorkingPrecision -> 110]
%t A199272 RealDigits[r]   (* A199272 *)
%Y A199272 Cf. A199170.
%K A199272 nonn,cons
%O A199272 0,1
%A A199272 _Clark Kimberling_, Nov 04 2011