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Question: Another inequality equation

Question:Another inequality equation

toandhsp 300
solve
November 13 2013
0

This is a problem of Russian in 2005: Solve inequality 

(3-x-sqrt(5-x^2))/(cos((2*x-7)/4)-cos((x-5)/4))>=0.

The problem can solve by hand. We only solve

(3-x-sqrt(5-x^2))/((2*x-7)/4-(x-5)/4) >=0.

I tried

eq1:=(3-x-sqrt(5-x^2))/((2*x-7)/4-(x-5)/4);

solve(eq1>=0,x);

I got

RealRange(1,Open(2)), RealRange(Open(2),5^(1/2)).

If I solve directly by

eq:=(3-x-sqrt(5-x^2))/(cos((2*x-7)/4)-cos((x-5)/4));

solve(eq>=0,x);

I don't get the exact answer. 

P.S. with Mathematica, I only use

Reduce[(3 - x - Sqrt[5 - x^2])/(Cos[(2 x - 7)/4] - Cos[(x - 5)/4]) >=
0, x, Reals]

 

 
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