Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -x=4-3(3x-8)
-
Equation x/9+x=-10/3
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Equation √(x^2-1)=2*x
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Equation 4(x-3)=x+6
- Express {x} in terms of y where:
- -6*x-20*y=8
- -9*x-15*y=-4
- 1*x+5*y=-11
- 12*x-14*y=20
-
Identical expressions
- 4sinx^ two -1 zero cosx- eight =0
- 4 sinus of x squared minus 10 co sinus of e of x minus 8 equally 0
- 4 sinus of x to the power of two minus 1 zero co sinus of e of x minus eight equally 0
- 4sinx2-10cosx-8=0
- 4sinx²-10cosx-8=0
- 4sinx to the power of 2-10cosx-8=0
- 4sinx^2-10cosx-8=O
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Similar expressions
- 4sinx^2+10cosx-8=0
- 4sinx^2-10cosx+8=0
4sinx^2-10cosx-8=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 4*sin (x) - 10*cos(x) - 8 = 0
$$4 \sin^{2}{\left(x \right)} - 10 \cos{\left(x \right)} - 8 = 0$$
Sum and product of roots
[src]
sum
-2*pi 2*pi / / ___\\ / / ___\\ / / ___\\ / / ___\\ ----- + ---- + 2*im\atanh\\/ 3 // - 2*I*re\atanh\\/ 3 // + - 2*im\atanh\\/ 3 // + 2*I*re\atanh\\/ 3 // 3 3
$$\left(- \frac{2 \pi}{3}\right) + \left(\frac{2 \pi}{3}\right) + \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}\right) + \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}\right)$$
=
0
$$0$$
product
-2*pi 2*pi / / ___\\ / / ___\\ / / ___\\ / / ___\\ ----- * ---- * 2*im\atanh\\/ 3 // - 2*I*re\atanh\\/ 3 // * - 2*im\atanh\\/ 3 // + 2*I*re\atanh\\/ 3 // 3 3
$$\left(- \frac{2 \pi}{3}\right) * \left(\frac{2 \pi}{3}\right) * \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}\right) * \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}\right)$$
=
2
2 / / / ___\\ / / ___\\\
16*pi *\- I*re\atanh\\/ 3 // + im\atanh\\/ 3 ///
-------------------------------------------------
9
$$\frac{16 \pi^{2} \left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}\right)^{2}}{9}$$
Rapid solution
[src]
-2*pi
x_1 = -----
3
$$x_{1} = - \frac{2 \pi}{3}$$
2*pi
x_2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
/ / ___\\ / / ___\\ x_3 = 2*im\atanh\\/ 3 // - 2*I*re\atanh\\/ 3 //
$$x_{3} = 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}$$
/ / ___\\ / / ___\\ x_4 = - 2*im\atanh\\/ 3 // + 2*I*re\atanh\\/ 3 //
$$x_{4} = - 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{3} \right)}\right)}$$
Numerical answer
[src]
x1 = -41.8879020478639
x2 = -79.5870138909414
x3 = -67.0206432765823
x4 = 2.0943951023932
x5 = 73.3038285837618
x6 = -83.7758040957278
x7 = -46.0766922526503
x8 = 67.0206432765823
x9 = 85.870199198121
x10 = 77.4926187885482
x11 = -23.0383461263252
x12 = 33.5103216382911
x13 = -10.471975511966
x14 = -14.6607657167524
x15 = -85.870199198121
x16 = -4.18879020478639
x17 = -60.7374579694027
x18 = -92.1533845053006
x19 = -58.6430628670095
x20 = 90.0589894029074
x21 = 4.18879020478639
x22 = 146.607657167524
x23 = -450.294947014537
x24 = -343.480796792484
x25 = 23.0383461263252
x26 = -71.2094334813686
x27 = -39.7935069454707
x28 = 10.471975511966
x29 = 27.2271363311115
x30 = 16.7551608191456
x31 = -64.9262481741891
x32 = -73.3038285837618
x33 = -54.4542726622231
x34 = -1296.43056838139
x35 = -8.37758040957278
x36 = 92.1533845053006
x37 = -77.4926187885482
x38 = -48.1710873550435
x39 = 48.1710873550435
x40 = -148.702052269917
x41 = -98.4365698124802
x42 = 96.342174710087
x43 = -16.7551608191456
x44 = 58.6430628670095
x45 = 20.943951023932
x46 = 83.7758040957278
x47 = 14.6607657167524
x48 = -29.3215314335047
x49 = 29.3215314335047
x50 = -90.0589894029074
x51 = 60.7374579694027
x52 = 54.4542726622231
x53 = -96.342174710087
x54 = 35.6047167406843
x55 = 39.7935069454707
x56 = 41.8879020478639
x57 = -8720441.26541496
x58 = -20.943951023932
x59 = -2.0943951023932
x60 = 46.0766922526503
x61 = -27.2271363311115
x62 = 64.9262481741891
x63 = 98.4365698124802
x64 = -35.6047167406843
x65 = -52.3598775598299
x66 = 71.2094334813686
x67 = -33.5103216382911
x68 = 4500.85507504298
x69 = 8.37758040957278
x70 = 79.5870138909414
x71 = 52.3598775598299
x71 = 52.3598775598299
The graph