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  • Similar expressions

  • 2*cos(x/2)^2-sqrt(3)*cos(x/2)=0

2*cos(x/2)^2+sqrt(3)*cos(x/2)=0 equation

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Numerical solution:

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The solution

You have entered [src] 
     2/x\     ___    /x\    
2*cos |-| + \/ 3 *cos|-| = 0
      \2/            \2/
$$2 \cos^{2}{\left(\frac{x}{2} \right)} + \sqrt{3} \cos{\left(\frac{x}{2} \right)} = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = pi
$$x_{1} = \pi$$ 
     5*pi
x2 = ----
      3
$$x_{2} = \frac{5 \pi}{3}$$ 
     7*pi
x3 = ----
      3
$$x_{3} = \frac{7 \pi}{3}$$ 
x4 = 3*pi
$$x_{4} = 3 \pi$$ 
x4 = 3*pi
Sum and product of roots [src] 
sum
     5*pi   7*pi       
pi + ---- + ---- + 3*pi
      3      3
$$3 \pi + \left(\frac{7 \pi}{3} + \left(\pi + \frac{5 \pi}{3}\right)\right)$$ 
=
8*pi
$$8 \pi$$ 
product
   5*pi 7*pi     
pi*----*----*3*pi
    3    3
$$3 \pi \frac{7 \pi}{3} \pi \frac{5 \pi}{3}$$ 
=
     4
35*pi 
------
  3
$$\frac{35 \pi^{4}}{3}$$ 
35*pi^4/3
Numerical answer [src] 
x1 = -91.106186954104
x2 = 84.8230016469244
x3 = -97.3893722612836
x4 = 91.106186954104
x5 = -82.7286065445312
x6 = 45.0294947014537
x7 = 57.5958653158129
x8 = -72.2566310325652
x9 = -47.1238898038469
x10 = -80.634211442138
x11 = 95.2949771588904
x12 = -45.0294947014537
x13 = 93.2005820564972
x14 = 70.162235930172
x15 = -55.5014702134197
x16 = 47.1238898038469
x17 = 40.8407044966673
x18 = -7.33038285837618
x19 = 65.9734457253857
x20 = -28.2743338823081
x21 = 15.707963267949
x22 = 28.2743338823081
x23 = -68.0678408277789
x24 = -40.8407044966673
x25 = 32.4631240870945
x26 = -15.707963267949
x27 = 55.5014702134197
x28 = 72.2566310325652
x29 = 3.14159265358979
x30 = -59.6902604182061
x31 = -19.8967534727354
x32 = 80.634211442138
x33 = 21.9911485751286
x34 = 7.33038285837618
x35 = -84.8230016469244
x36 = 78.5398163397448
x37 = 9.42477796076938
x38 = 5.23598775598299
x39 = 30.3687289847013
x40 = 82.7286065445312
x41 = -53.4070751110265
x42 = 42.9350995990605
x43 = 103.672557568463
x44 = -95.2949771588904
x45 = -9.42477796076938
x46 = 17.8023583703422
x47 = -93.2005820564972
x48 = -34.5575191894877
x49 = -3.14159265358979
x50 = -17.8023583703422
x51 = -32.4631240870945
x52 = -5.23598775598299
x53 = -21.9911485751286
x54 = -57.5958653158129
x55 = -42.9350995990605
x56 = -78.5398163397448
x57 = 68.0678408277789
x58 = -30.3687289847013
x59 = 97.3893722612836
x60 = 19.8967534727354
x61 = 59.6902604182061
x62 = 53.4070751110265
x63 = 34.5575191894877
x64 = -65.9734457253857
x65 = -70.162235930172
x65 = -70.162235930172
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