Mister Exam
ctgx/3-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cot{\left(x \right)}}{3} - 1 = 0$$
transform
$$\frac{\cot{\left(x \right)}}{3} - 1 = 0$$
$$\frac{\cot{\left(x \right)}}{3} - 1 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{3} = 1$$
Divide both parts of the equation by 1/3
We get the answer: w = 3
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\frac{\cot{\left(x \right)}}{3} - 1 = 0$$
transform
$$\frac{\cot{\left(x \right)}}{3} - 1 = 0$$
$$\frac{\cot{\left(x \right)}}{3} - 1 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{3} = 1$$
Divide both parts of the equation by 1/3
w = 1 / (1/3)
We get the answer: w = 3
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
Sum and product of roots
[src]
sum
acot(3)
$$\operatorname{acot}{\left(3 \right)}$$
=
acot(3)
$$\operatorname{acot}{\left(3 \right)}$$
product
acot(3)
$$\operatorname{acot}{\left(3 \right)}$$
=
acot(3)
$$\operatorname{acot}{\left(3 \right)}$$
acot(3)
Numerical answer
[src]
x1 = -27.9525833279115
x2 = 339.613757142094
x3 = 66.2951962797823
x4 = 22.3128991295252
x5 = -21.6693980207319
x6 = -9.10302740637274
x7 = 78.8615668941415
x8 = -5.96143475278294
x9 = -71.9348804781686
x10 = 85.1447522013211
x11 = -18.5278053671421
x12 = -37.3773612886809
x13 = -185.032216007401
x14 = -87.6428437461176
x15 = -65.651695170989
x16 = 44.3040477046537
x17 = -62.5101025173992
x18 = 38.0208623974742
x19 = 16.0297138223456
x20 = 60.0120109726027
x21 = -56.2269172102196
x22 = 88.2863448549109
x23 = 82.0031595477313
x24 = 28.5960844367048
x25 = -93.9260290532972
x26 = 72.5783815869619
x27 = -49.9437319030401
x28 = -78.2180657853482
x29 = -34.2357686350911
x30 = 1574.25967000288
x31 = 97.7111228156802
x32 = -100.209214360477
x33 = -43.6605465958605
x34 = -1297.15601537819
x34 = -1297.15601537819