Mister Exam
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How to use it?
- Equation:
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Equation (x-2)^2+(x-3)^2=2x^2
-
Equation 3x^2-27=0
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Equation sin(x+pi/3)=0
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Equation sin(x)=-√3/2
- Express {x} in terms of y where:
- -6*x-2*y=-10
- 18*x+14*y=-11
- 4*x+16*y=6
- sin(xy)+cos(xy)=tg(x+y)
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Identical expressions
- (cos(2x)-3cos(x)- one)/(sqrt(2sin(x)- one))= zero
- ( co sinus of e of (2x) minus 3 co sinus of e of (x) minus 1) divide by ( square root of (2 sinus of (x) minus 1)) equally 0
- ( co sinus of e of (2x) minus 3 co sinus of e of (x) minus one) divide by ( square root of (2 sinus of (x) minus one)) equally zero
- (cos(2x)-3cos(x)-1)/(√(2sin(x)-1))=0
- cos2x-3cosx-1/sqrt2sinx-1=0
- (cos(2x)-3cos(x)-1)/(sqrt(2sin(x)-1))=O
- (cos(2x)-3cos(x)-1) divide by (sqrt(2sin(x)-1))=0
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Similar expressions
- (cos(2x)-3cos(x)+1)/(sqrt(2sin(x)-1))=0
- (cos(2x)+3cos(x)-1)/(sqrt(2sin(x)-1))=0
- (cos(2x)-3cos(x)-1)/(sqrt(2sin(x)+1))=0
- (cos(2x)-3cosx-1)/(sqrt(2sinx-1))=0
(cos(2x)-3cos(x)-1)/(sqrt(2sin(x)-1))=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
cos(2*x) - 3*cos(x) - 1
----------------------- = 0
______________
\/ 2*sin(x) - 1
$$\frac{\left(- 3 \cos{\left(x \right)} + \cos{\left(2 x \right)}\right) - 1}{\sqrt{2 \sin{\left(x \right)} - 1}} = 0$$
Rapid solution
[src]
-2*pi
x1 = -----
3
$$x_{1} = - \frac{2 \pi}{3}$$
2*pi
x2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
/ ___\ x3 = -I*log\2 - \/ 3 /
$$x_{3} = - i \log{\left(2 - \sqrt{3} \right)}$$
/ ___\ x4 = -I*log\2 + \/ 3 /
$$x_{4} = - i \log{\left(\sqrt{3} + 2 \right)}$$
x4 = -i*log(sqrt(3) + 2)
Sum and product of roots
[src]
sum
2*pi 2*pi / ___\ / ___\ - ---- + ---- - I*log\2 - \/ 3 / - I*log\2 + \/ 3 / 3 3
$$- i \log{\left(\sqrt{3} + 2 \right)} + \left(\left(- \frac{2 \pi}{3} + \frac{2 \pi}{3}\right) - i \log{\left(2 - \sqrt{3} \right)}\right)$$
=
/ ___\ / ___\ - I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$
product
-2*pi 2*pi / / ___\\ / / ___\\ -----*----*\-I*log\2 - \/ 3 //*\-I*log\2 + \/ 3 // 3 3
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)} - \frac{2 \pi}{3} \frac{2 \pi}{3}$$
=
2 / ___\ / ___\
4*pi *log\2 + \/ 3 /*log\2 - \/ 3 /
-----------------------------------
9
$$\frac{4 \pi^{2} \log{\left(2 - \sqrt{3} \right)} \log{\left(\sqrt{3} + 2 \right)}}{9}$$
4*pi^2*log(2 + sqrt(3))*log(2 - sqrt(3))/9
Numerical answer
[src]
x1 = 64.9262481741891
x2 = -90.0589894029074
x3 = -46.0766922526503
x4 = -41.8879020478639
x5 = -83.7758040957278
x6 = -92.1533845053006
x7 = -58.6430628670095
x8 = -54.4542726622231
x9 = 60.7374579694027
x10 = -23.0383461263252
x11 = -85.870199198121
x12 = 23.0383461263252
x13 = -64.9262481741891
x14 = -29.3215314335047
x15 = -4.18879020478639
x16 = 20.943951023932
x17 = 2.0943951023932
x18 = 77.4926187885482
x19 = 90.0589894029074
x20 = 29.3215314335047
x21 = -16.7551608191456
x22 = 48.1710873550435
x23 = -20.943951023932
x24 = -60.7374579694027
x25 = 16.7551608191456
x26 = -77.4926187885482
x27 = 39.7935069454707
x28 = -39.7935069454707
x29 = -2.0943951023932
x30 = -10.471975511966
x31 = -35.6047167406843
x32 = -79.5870138909414
x33 = 14.6607657167524
x34 = -6.28318530717959 + 1.31695789692482*i
x35 = 37.6991118430775 + 1.31695789692482*i
x36 = 58.6430628670095
x37 = -25.1327412287183 + 1.31695789692482*i
x38 = 79.5870138909414
x39 = 73.3038285837618
x40 = 52.3598775598299
x41 = 8.37758040957278
x42 = 54.4542726622231
x43 = -71.2094334813686
x44 = 33.5103216382911
x45 = -52.3598775598299
x46 = -98.4365698124802
x47 = 71.2094334813686
x48 = 83.7758040957278
x49 = -33.5103216382911
x50 = 4.18879020478639
x51 = 98.4365698124802
x52 = 96.342174710087
x53 = -8.37758040957278
x54 = -14.6607657167524
x55 = 35.6047167406843
x56 = -27.2271363311115
x57 = -96.342174710087
x58 = 10.471975511966
x59 = 92.1533845053006
x60 = -73.3038285837618
x61 = 67.0206432765823
x62 = -48.1710873550435
x63 = 85.870199198121
x64 = -67.0206432765823
x65 = 41.8879020478639
x66 = 81.6814089933346 + 1.31695789692482*i
x67 = 46.0766922526503
x68 = 27.2271363311115
x68 = 27.2271363311115