Mister Exam
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How to use it?
- Equation:
-
Equation sqrt(x+2*sqrt(x-1))+sqrt(x-2*sqrt(x-1))=2
-
Equation k^2-2*k-3=0
- Equation ctgx=-√3
-
Equation (y^2)/(y^2-6y)=4(3-2y)/(y(6-y))
- Express {x} in terms of y where:
- -10*x+18*y=6
- 9*x-18*y=6
- -1*x+19*y=-10
- 4*x+13*y=13
- Integral of d{x}:
- ctgx
- Derivative of:
-
ctgx
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Identical expressions
- ctgx=-√ three
- ctgx equally minus √3
- ctgx equally minus √ three
-
Similar expressions
- arctg(x-1)+arctg(x)+arctg(x+1)=arctg(3x)
- tg^2(x)+ctg^2(x)+3*(tg(x)+ctg(x))+4=0
- ctg(x/3)=-(√3/2)
- arctg(x/y)
- ctgx=+√3
ctgx=-√3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cot{\left(x \right)} = - \sqrt{3}$$
transform
$$\cot{\left(x \right)} - 1 + \sqrt{3} = 0$$
$$\cot{\left(x \right)} - 1 + \sqrt{3} = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Expand brackets in the left part
Move free summands (without w)
from left part to right part, we given:
$$w + \sqrt{3} = 1$$
Divide both parts of the equation by (w + sqrt(3))/w
We get the answer: w = 1 - sqrt(3)
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\cot{\left(x \right)} = - \sqrt{3}$$
transform
$$\cot{\left(x \right)} - 1 + \sqrt{3} = 0$$
$$\cot{\left(x \right)} - 1 + \sqrt{3} = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Expand brackets in the left part
-1 + w + sqrt3 = 0
Move free summands (without w)
from left part to right part, we given:
$$w + \sqrt{3} = 1$$
Divide both parts of the equation by (w + sqrt(3))/w
w = 1 / ((w + sqrt(3))/w)
We get the answer: w = 1 - sqrt(3)
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
Sum and product of roots
[src]
sum
-pi ---- 6
$$- \frac{\pi}{6}$$
=
-pi ---- 6
$$- \frac{\pi}{6}$$
product
-pi ---- 6
$$- \frac{\pi}{6}$$
=
-pi ---- 6
$$- \frac{\pi}{6}$$
-pi/6
Numerical answer
[src]
x1 = 71.733032256967
x2 = 78.0162175641465
x3 = -57.0722665402146
x4 = -79.0634151153431
x5 = 81.1578102177363
x6 = 100.007366139275
x7 = -25.6563400043166
x8 = -31.9395253114962
x9 = -60.2138591938044
x10 = -53.9306738866248
x11 = -97.9129710368819
x12 = -72.7802298081635
x13 = -75.9218224617533
x14 = 90.5825881785057
x15 = -82.2050077689329
x16 = 93.7241808320955
x17 = -19.3731546971371
x18 = 84.2994028713261
x19 = 59.1666616426078
x20 = -69.6386371545737
x21 = -16.2315620435473
x22 = -22.5147473507269
x23 = -13.0899693899575
x24 = 40.317105721069
x25 = -44.5058959258554
x26 = -28.7979326579064
x27 = -41.3643032722656
x28 = 68.5914396033772
x29 = 24.60914245312
x30 = 18.3259571459405
x31 = -6.80678408277789
x32 = -85.3466004225227
x33 = -88.4881930761125
x34 = 56.025068989018
x35 = -47.6474885794452
x36 = -9.94837673636768
x37 = -91.6297857297023
x38 = 46.6002910282486
x39 = -3.66519142918809
x40 = 37.1755130674792
x41 = 96.8657734856853
x42 = 34.0339204138894
x43 = 12.0427718387609
x44 = 5.75958653158129
x45 = -66.497044500984
x46 = -50.789081233035
x47 = -0.523598775598299
x48 = 43.4586983746588
x49 = 30.8923277602996
x50 = 49.7418836818384
x51 = 52.8834763354282
x52 = -63.3554518473942
x53 = 74.8746249105567
x54 = -94.7713783832921
x55 = 2.61799387799149
x56 = 65.4498469497874
x57 = 62.3082542961976
x58 = 8.90117918517108
x59 = 87.4409955249159
x60 = 21.4675497995303
x61 = -38.2227106186758
x62 = 27.7507351067098
x63 = 15.1843644923507
x63 = 15.1843644923507