Mister Exam
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How to use it?
- Equation:
-
Equation x=x/2+1
-
Equation (7-x)^2=(x+16)^2
-
Equation x^4-5x^2-6=0
- Equation 3cos²x+10sinx-10=0
- Express {x} in terms of y where:
- 16*x+7*y=8
- 17*x-11*y=2
- -16*x-7*y=-5
- 1*x-19*y=-10
-
Identical expressions
- tg²x-5tgx- six = zero
- tg²x minus 5tgx minus 6 equally 0
- tg²x minus 5tgx minus six equally zero
- tg²x-5tgx-6=O
-
Similar expressions
- tg²x+5tgx-6=0
- tg²x-5tgx+6=0
tg²x-5tgx-6=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2 tan (x) - 5*tan(x) - 6 = 0
$$\tan^{2}{\left(x \right)} - 5 \tan{\left(x \right)} - 6 = 0$$
Detail solution
Given the equation:
$$\tan^{2}{\left(x \right)} - 5 \tan{\left(x \right)} - 6 = 0$$
Transform
$$\tan^{2}{\left(x \right)} - 5 \tan{\left(x \right)} - 6 = 0$$
$$\left(\tan{\left(x \right)} - 6\right) \left(\tan{\left(x \right)} + 1\right) = 0$$
Consider each factor separately
$$\tan{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$\tan{\left(x \right)} = -1$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$\tan{\left(x \right)} - 6 = 0$$
- this is the simplest trigonometric equation
Move $-6$ to right part of the equation
with the change of sign in $-6$
We get:
$$\tan{\left(x \right)} = 6$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(6 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(6 \right)}$$
, where n - is a integer
The final answer:
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{2} = \pi n + \operatorname{atan}{\left(6 \right)}$$
$$\tan^{2}{\left(x \right)} - 5 \tan{\left(x \right)} - 6 = 0$$
Transform
$$\tan^{2}{\left(x \right)} - 5 \tan{\left(x \right)} - 6 = 0$$
$$\left(\tan{\left(x \right)} - 6\right) \left(\tan{\left(x \right)} + 1\right) = 0$$
Consider each factor separately
Step
$$\tan{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$\tan{\left(x \right)} = -1$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Step
$$\tan{\left(x \right)} - 6 = 0$$
- this is the simplest trigonometric equation
Move $-6$ to right part of the equation
with the change of sign in $-6$
We get:
$$\tan{\left(x \right)} = 6$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(6 \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(6 \right)}$$
, where n - is a integer
The final answer:
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{2} = \pi n + \operatorname{atan}{\left(6 \right)}$$
Rapid solution
[src]
-pi
x_1 = ----
4
$$x_{1} = - \frac{\pi}{4}$$
x_2 = atan(6)
$$x_{2} = \operatorname{atan}{\left(6 \right)}$$
Sum and product of roots
[src]
sum
-pi ---- + atan(6) 4
$$\left(- \frac{\pi}{4}\right) + \left(\operatorname{atan}{\left(6 \right)}\right)$$
=
pi - -- + atan(6) 4
$$- \frac{\pi}{4} + \operatorname{atan}{\left(6 \right)}$$
product
-pi ---- * atan(6) 4
$$\left(- \frac{\pi}{4}\right) * \left(\operatorname{atan}{\left(6 \right)}\right)$$
=
-pi*atan(6)
------------
4
$$- \frac{\pi \operatorname{atan}{\left(6 \right)}}{4}$$
Numerical answer
[src]
x1 = 99.7455667514759
x2 = 33.7721210260903
x3 = 18.0641577581413
x4 = 79.9454639891251
x5 = 27.4889357189107
x6 = -101.316363078271
x7 = -13.3517687777566
x8 = -3.92699081698724
x9 = 68.329640215578
x10 = -79.3252145031423
x11 = -38.484510006475
x12 = 30.6305283725005
x13 = 36.9137136796801
x14 = -52.0014274616462
x15 = -19.6349540849362
x16 = -7.06858347057703
x17 = 80.8960108299372
x18 = -45.7182421544666
x19 = 64.2375007211761
x20 = -57.3340659280137
x21 = 77.7544181763474
x22 = -8.01913031138911
x23 = -35.3429173528852
x24 = 2.35619449019234
x25 = -82.4668071567321
x26 = -29.0597320457056
x27 = -32.2013246992954
x28 = 21.2057504117311
x29 = 57.9543154139965
x30 = -76.1836218495525
x31 = -73.0420291959627
x32 = 74.6128255227576
x33 = -1.73594500420952
x34 = -66.7588438887831
x35 = -67.7093907295952
x36 = 86.2286492963047
x37 = 24.3473430653209
x38 = -0.785398163397448
x39 = -25.9181393921158
x40 = -41.6261026600648
x41 = -98.174770424681
x42 = -47.9092879672443
x43 = 20.255203570919
x44 = 5.49778714378214
x45 = -95.0331777710912
x46 = 8.63937979737193
x47 = -16.4933614313464
x48 = -69.9004365423729
x49 = 11.7809724509617
x50 = -22.776546738526
x51 = 43.1968989868597
x52 = -44.7676953136546
x53 = -23.7270935793381
x54 = 46.3384916404494
x55 = 71.4712328691678
x56 = 96.6039740978861
x57 = 14.9225651045515
x58 = -63.6172512351933
x59 = 55.7632696012188
x60 = -51.0508806208341
x61 = -60.4756585816035
x62 = -91.8915851175014
x63 = -10.2101761241668
x64 = 90.3207887907066
x65 = -95.9837246119033
x66 = 58.9048622548086
x67 = -73.9925760367748
x68 = 40.0553063332699
x69 = -85.6083998103219
x70 = 49.4800842940392
x71 = 13.9720182637394
x72 = -54.1924732744239
x73 = 65.1880475619882
x74 = 62.0464549083984
x75 = 42.2463521460476
x76 = 35.963166838868
x77 = 52.621676947629
x78 = -30.0102788865177
x79 = -88.7499924639117
x80 = 87.1791961371168
x81 = 93.4623814442964
x82 = 84.037603483527
x82 = 84.037603483527
The graph