# Reduce applied to large inequality doesn't work

I want to solve the next inequality :

Reduce[16 m5^2 + ma^2 + mp^2 -
Sqrt[(-16 m5^2 - ma^2 - mp^2)^2 - 4 (ma^2 mp^2 - 16 m5^2 q^2)] >
0 && m5 > 0  && q > 0 && ma > 0 && mp > 0, {q, m5}, Reals]


Where

ma = Sqrt[-2 (M^2 -
2 (3 k1 + k2) (Sqrt[(c + M^2 + 2 m5^2)/(2 (k1 + k2))] +
m b/(2 (c + M^2 + 2 m5^2)))^2 - c + 2 m5^2)];
mp = Sqrt[
2 b m ((Sqrt[(c + M^2 + 2 m5^2)/(2 (k1 + k2))] +
m b/(2 (c + M^2 + 2 m5^2)))^-1) ];


and

c = -44687.4; b = 161594.;k1 = 16.485; k2 = -13.1313; m = 5.5; M = 300;


But Mathematica solves it several hours and unfortunately without result. May you prompt where I mistake?

Reduce[m5 < (ma mp)/(4 q) && m5 > 0  && q > 0 && ma > 0 &&
mp > 0, m5, Reals]


Then I found solution but answer will be very large one:

q > 0 && 0 < m5 <
Root[-2.27376*10^160 + (-6.7933*10^156 -
1.05104*10^151 q^2) #1^2 + (-8.26796*10^152 -
1.80431*10^147 q^2 +
2.59679*10^142 q^4) #1^4 + (-5.29216*10^148 -
1.15366*10^143 q^2 +
5.7805*10^138 q^4) #1^6 + (-1.88976*10^144 -
3.26407*10^138 q^2 +
5.12469*10^134 q^4) #1^8 + (-3.58288*10^139 -
3.45762*10^133 q^2 +
2.26515*10^130 q^4) #1^10 + (-2.82458*10^134 +
4.99895*10^125 q^4) #1^12 + 4.41285*10^120 q^4 #1^14 &, 2]


May it simplify?

• What sort of result are you seeking? – bbgodfrey Apr 29 '17 at 20:33
• @bbgodfrey For example form like q<10*m5 – illuminates Apr 29 '17 at 22:06

Rewrite to Accommodate Revised Question

The solution provided in the revised question (designated here as ff) can be plotted by

ParametricPlot[{Log10[Evaluate[ff[[2, 3]]] /. q -> 10^logq], logq}, {logq, -.55, 9.53},
AspectRatio -> 1/GoldenRatio,
AxesLabel -> {"Log10[m5]", "Log10[q]"}, ImageSize -> 400, AxesOrigin -> {-5, -.55}] This is, of course, equivalent to the simpler

LogLogPlot[ma mp/(4 m5), {m5, 10^-5, 10^8}, AxesLabel -> {"m5", "q"}] • Thank you, but yours resalt is for ma=... and mp=... without sqrt: ma = Sqrt[...] and Sqrt[...]. I add it after several hours as I placed question. It is my fault. You may ask me, what's the problem? Problem is that inequality in this case is: – illuminates Apr 30 '17 at 9:04
• 0 < m5 < Root[-2.27376*10^160 + (-6.7933*10^156 - 1.05104*10^151 q^2) #1^2 + (-8.26796*10^152 - 1.80431*10^147 q^2 + 2.59679*10^142 q^4) #1^4 + (-5.29216*10^148 - 1.15366*10^143 q^2 + 5.7805*10^138 q^4) #1^6 + (-1.88976*10^144 - 3.26407*10^138 q^2 + 5.12469*10^134 q^4) #1^8 + (-3.58288*10^139 - 3.45762*10^133 q^2 + 2.26515*10^130 q^4) #1^10 + (-2.82458*10^134 + 4.99895*10^125 q^4) #1^12 + 4.41285*10^120 q^4 #1^14 &, 2] – illuminates Apr 30 '17 at 9:04
• This result can't be plotted – illuminates Apr 30 '17 at 9:04

It can be plotted. You can use PlotRegion to show the region.

In:

c = -44687.4; b = 161594.; k1 = 16.485; k2 = -13.1313; m = 5.5; M = \
300;
ma = Sqrt[-2 (M^2 -
2 (3 k1 +
k2) (Sqrt[(c + M^2 + 2 m5^2)/(2 (k1 + k2))] +
m b/(2 (c + M^2 + 2 m5^2)))^2 - c + 2 m5^2)];
mp = Sqrt[
2 b m ((Sqrt[(c + M^2 + 2 m5^2)/(2 (k1 + k2))] +
m b/(2 (c + M^2 + 2 m5^2)))^-1)];

f = 16 m5^2 + ma^2 + mp^2 -
Sqrt[(-16 m5^2 - ma^2 - mp^2)^2 - 4 (ma^2 mp^2 - 16 m5^2 q^2)];
RegionPlot[f > 0, {m5, 0, 10000}, {q, 0, 1000}, Axes -> True,
FrameLabel -> {"m5", "q"}]