Mister Exam
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How to use it?
- Equation:
-
Equation sin(6x)-cos(3x)=0
-
Equation ctg²5x-ctg5x=0
- Equation (d+7)(-d-7)+(2d-1)
-
Equation cos(pi*x)=0
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 4*x-16*y=6
- 5*x+5*y=20
- 10*x-1*y=10
-
Identical expressions
- ctg²5x-ctg5x= zero
- ctg²5x minus ctg5x equally 0
- ctg²5x minus ctg5x equally zero
- ctg²5x-ctg5x=O
-
Similar expressions
- ctg²5x+ctg5x=0
ctg²5x-ctg5x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
25 cot (x) - cot(5*x) = 0
$$\cot^{25}{\left(x \right)} - \cot{\left(5 x \right)} = 0$$
Sum and product of roots
[src]
sum
-3*pi -pi -pi pi pi 3*pi ----- + ---- + ---- + -- + -- + ---- 4 2 4 4 2 4
$$\left(- \frac{3 \pi}{4}\right) + \left(- \frac{\pi}{2}\right) + \left(- \frac{\pi}{4}\right) + \left(\frac{\pi}{4}\right) + \left(\frac{\pi}{2}\right) + \left(\frac{3 \pi}{4}\right)$$
=
0
$$0$$
product
-3*pi -pi -pi pi pi 3*pi ----- * ---- * ---- * -- * -- * ---- 4 2 4 4 2 4
$$\left(- \frac{3 \pi}{4}\right) * \left(- \frac{\pi}{2}\right) * \left(- \frac{\pi}{4}\right) * \left(\frac{\pi}{4}\right) * \left(\frac{\pi}{2}\right) * \left(\frac{3 \pi}{4}\right)$$
=
6 -9*pi ------ 1024
$$- \frac{9 \pi^{6}}{1024}$$
Rapid solution
[src]
-3*pi
x_1 = -----
4
$$x_{1} = - \frac{3 \pi}{4}$$
-pi
x_2 = ----
2
$$x_{2} = - \frac{\pi}{2}$$
-pi
x_3 = ----
4
$$x_{3} = - \frac{\pi}{4}$$
pi
x_4 = --
4
$$x_{4} = \frac{\pi}{4}$$
pi
x_5 = --
2
$$x_{5} = \frac{\pi}{2}$$
3*pi
x_6 = ----
4
$$x_{6} = \frac{3 \pi}{4}$$
Numerical answer
[src]
x1 = 48.0662993480935
x2 = -58.1194640914112
x3 = -93.4623814442964
x4 = -71.4712328691678
x5 = -5.49778714378214
x6 = -26.075150772965
x7 = 36.1283155162826
x8 = 39.8982949524207
x9 = -61.8894435275492
x10 = -51.8362787842316
x11 = 24.1903316844717
x12 = -92.0485964983506
x13 = 55.7632696012188
x14 = -67.5442420521806
x15 = -54.1924732744239
x16 = -63.7742626160425
x17 = 68.1726288347288
x18 = -99.7455667514759
x19 = -32.2013246992954
x20 = 54.3494846552731
x21 = 82.4668071567321
x22 = -45.553093477052
x23 = 46.1814802596003
x24 = 90.1637774098574
x25 = 33.7721210260903
x26 = -19.7919654657854
x27 = -83.8805921026778
x28 = 64.4026493985908
x29 = 58.1194640914112
x30 = -27.4889357189107
x31 = -77.7544181763474
x32 = 80.1106126665397
x33 = 99.7455667514759
x34 = 77.7544181763474
x35 = 74.4558141419084
x36 = 86.3937979737193
x37 = 16.4933614313464
x38 = -80.1106126665397
x39 = 96.4469627170369
x40 = 14.1371669411541
x41 = 7.85398163397448
x42 = 4.08400219783644
x43 = -39.8982949524207
x44 = 26.075150772965
x45 = 61.8894435275492
x46 = 92.0485964983506
x47 = -85.7654111911711
x48 = 52.4646655667798
x49 = 11.7809724509617
x50 = -48.0662993480935
x51 = -89.5353906273091
x52 = -95.8185759344887
x53 = -4.08400219783644
x54 = -36.1283155162826
x55 = 70.0574479232221
x56 = 2.19918310934315
x57 = -76.1836218495525
x58 = 17.9071463772921
x59 = -14.1371669411541
x60 = 60.4756585816035
x61 = -23.5619449019235
x62 = 76.3406332304017
x63 = -73.8274273593601
x64 = 29.845130209103
x65 = -41.783114040914
x66 = 32.3583360801446
x67 = -70.0574479232221
x68 = -98.174770424681
x69 = -49.4800842940392
x70 = -1.5707963267949
x71 = -55.7632696012188
x72 = 42.4115008234622
x73 = -10.2101761241668
x74 = 20.4203522483337
x75 = 98.3317818055302
x76 = -29.845130209103
x77 = -33.7721210260903
x78 = 38.484510006475
x79 = -17.9071463772921
x80 = -7.85398163397448
x81 = 11.6239610701125
x81 = 11.6239610701125
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