Mister Exam
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How to use it?
- Equation:
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Equation x^4=(4*x-21)^2
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Equation (x+2)^2+(x-3)^2=2x^2
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Equation sin(x)=3/2
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Equation 13-6(3-x)=25
- Express {x} in terms of y where:
- -19*x-14*y=-8
- -16*x+7*y=-5
- -2*x-1*y=-8
- (x^2+y^2-1)^3-x^2*y^3=0
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Identical expressions
- 3sin^2x-7sinx×cosx+2cos^2x= zero
- 3 sinus of squared x minus 7 sinus of x× co sinus of e of x plus 2 co sinus of e of squared x equally 0
- 3 sinus of squared x minus 7 sinus of x× co sinus of e of x plus 2 co sinus of e of squared x equally zero
- 3sin2x-7sinx×cosx+2cos2x=0
- 3sin²x-7sinx×cosx+2cos²x=0
- 3sin to the power of 2x-7sinx×cosx+2cos to the power of 2x=0
- 3sin^2x-7sinx×cosx+2cos^2x=O
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Similar expressions
- 3sin^2x+7sinx×cosx+2cos^2x=0
- 3sin^2x-7sinx×cosx-2cos^2x=0
3sin^2x-7sinx×cosx+2cos^2x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 3*sin (x) - 7*sin(x)*cos(x) + 2*cos (x) = 0
$$\left(3 \sin^{2}{\left(x \right)} - 7 \sin{\left(x \right)} \cos{\left(x \right)}\right) + 2 \cos^{2}{\left(x \right)} = 0$$
Sum and product of roots
[src]
sum
/ ___\ / ___\
|1 \/ 5 | |1 \/ 5 | / ____\ / ____\
- 2*atan|- - -----| - 2*atan|- + -----| - 2*atan\3 - \/ 10 / - 2*atan\3 + \/ 10 /
\2 2 / \2 2 /
$$- 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)} + \left(\left(- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right) - 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}\right)$$
=
/ ___\ / ___\
|1 \/ 5 | |1 \/ 5 | / ____\ / ____\
- 2*atan|- + -----| - 2*atan|- - -----| - 2*atan\3 + \/ 10 / - 2*atan\3 - \/ 10 /
\2 2 / \2 2 /
$$- 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$
product
/ ___\ / ___\
|1 \/ 5 | |1 \/ 5 | / ____\ / ____\
-2*atan|- - -----|*-2*atan|- + -----|*-2*atan\3 - \/ 10 /*-2*atan\3 + \/ 10 /
\2 2 / \2 2 /
$$- 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \left(- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right) \left(- 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}\right) \left(- 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}\right)$$
=
/ ___\ / ___\
|1 \/ 5 | |1 \/ 5 | / ____\ / ____\
16*atan|- + -----|*atan|- - -----|*atan\3 + \/ 10 /*atan\3 - \/ 10 /
\2 2 / \2 2 /
$$16 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(3 - \sqrt{10} \right)} \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
16*atan(1/2 + sqrt(5)/2)*atan(1/2 - sqrt(5)/2)*atan(3 + sqrt(10))*atan(3 - sqrt(10))
Rapid solution
[src]
/ ___\
|1 \/ 5 |
x1 = -2*atan|- - -----|
\2 2 /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$
/ ___\
|1 \/ 5 |
x2 = -2*atan|- + -----|
\2 2 /
$$x_{2} = - 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
/ ____\ x3 = -2*atan\3 - \/ 10 /
$$x_{3} = - 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}$$
/ ____\ x4 = -2*atan\3 + \/ 10 /
$$x_{4} = - 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
x4 = -2*atan(3 + sqrt(10))
Numerical answer
[src]
x1 = 95.3549283254879
x2 = -14.6008145501549
x3 = -78.2180657853482
x4 = 82.0031595477313
x5 = 26.2398899465124
x6 = 63.93900178959
x7 = 44.3040477046537
x8 = -37.3773612886809
x9 = -65.651695170989
x10 = -5.96143475278294
x11 = -46.0167410860528
x12 = 35.6646679072818
x13 = 9.74652851516602
x14 = 8973.49576737024
x15 = -39.7335557788732
x16 = -49.9437319030401
x17 = -87.6428437461176
x18 = 88.2863448549109
x19 = 100.85271546927
x20 = -1294649.22539564
x21 = 79.6469650575389
x22 = 22.3128991295252
x23 = -9.10302740637274
x24 = -93.9260290532972
x25 = 72.5783815869619
x26 = 73.3637797503593
x27 = 51.3726311752308
x28 = 56.8704183190129
x29 = 48.231038521641
x30 = 50.5872330118333
x31 = -52.2999263932324
x32 = -71.9348804781686
x33 = -59.3685098638094
x34 = 34.8792697438844
x35 = -34.2357686350911
x36 = -97.067621706887
x37 = -89.9990382363099
x38 = 38.0208623974742
x39 = 13.6735193321533
x40 = -36.5919631252834
x41 = -68.0078896611814
x42 = -74.2910749683609
x43 = 6.60493586157623
x44 = 12.8881211687558
x45 = -80.5742602755405
x46 = 16.0297138223456
x47 = -81.359658438938
x48 = 41.9478532144614
x49 = 66.2951962797823
x50 = 29.3814826001022
x51 = -24.0255925109243
x52 = -100.209214360477
x53 = 28.5960844367048
x54 = 0.321750554396642
x55 = 94.5695301620904
x56 = -2.0344439357957
x57 = -27.9525833279115
x58 = 78.8615668941415
x59 = 4627.88772929216
x60 = -43.6605465958605
x61 = 4.24874137138388
x62 = -8.31762924297529
x63 = -42.875148432463
x64 = -56.2269172102196
x65 = -17.7424072037447
x66 = -31.0941759815013
x67 = -15.3862127135523
x68 = 70.2221870967695
x69 = 85.9301503647185
x70 = -96.2822235434895
x71 = 60.0120109726027
x72 = -1146.35956800588
x73 = -58.583111700412
x74 = -53.0853245566298
x75 = 57.6558164824104
x76 = -30.3087778181038
x77 = -75.0764731317584
x78 = 7.39033402497368
x79 = -83.7158529291303
x80 = -61.7247043540018
x81 = 92.2133356718981
x82 = 19.9567046393328
x83 = -21.6693980207319
x83 = -21.6693980207319