Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 9x−9(x+1)=−2x
-
Equation -25-x=-17
-
Equation -x^2+5*x-6=0
- Equation x-y=7
- Express {x} in terms of y where:
- 7*x-1*y=-7
- 10*x-15*y=16
- 10*x-18*y=3
- 19*x-12*y=16
-
Identical expressions
- sqrt(two *cot(x))- one = zero
- square root of (2 multiply by cotangent of (x)) minus 1 equally 0
- square root of (two multiply by cotangent of (x)) minus one equally zero
- √(2*cot(x))-1=0
- sqrt(2cot(x))-1=0
- sqrt2cotx-1=0
- sqrt(2*cot(x))-1=O
-
Similar expressions
- sqrt(2*cot(x))+1=0
sqrt(2*cot(x))-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{2 \cot{\left(x \right)}} - 1 = 0$$
transform
$$\sqrt{2} \sqrt{\cot{\left(x \right)}} - 1 = 0$$
$$\sqrt{2 \cot{\left(x \right)}} - 1 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Given the equation
$$\sqrt{2} \sqrt{w} - 1 = 0$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{2 w}\right)^{2} = 1^{2}$$
or
$$2 w = 1$$
Divide both parts of the equation by 2
We get the answer: w = 1/2
The final answer:
$$w_{1} = \frac{1}{2}$$
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\sqrt{2 \cot{\left(x \right)}} - 1 = 0$$
transform
$$\sqrt{2} \sqrt{\cot{\left(x \right)}} - 1 = 0$$
$$\sqrt{2 \cot{\left(x \right)}} - 1 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Given the equation
$$\sqrt{2} \sqrt{w} - 1 = 0$$
Because equation degree is equal to = 1/2 - does not contain even numbers in the numerator, then
the equation has single real root.
We raise the equation sides to 2-th degree:
We get:
$$\left(\sqrt{2 w}\right)^{2} = 1^{2}$$
or
$$2 w = 1$$
Divide both parts of the equation by 2
w = 1 / (2)
We get the answer: w = 1/2
The final answer:
$$w_{1} = \frac{1}{2}$$
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
Sum and product of roots
[src]
sum
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
=
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
product
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
=
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
acot(1/2)
Rapid solution
[src]
x1 = acot(1/2)
$$x_{1} = \operatorname{acot}{\left(\frac{1}{2} \right)}$$
x1 = acot(1/2)
Numerical answer
[src]
x1 = 35.6646679072818
x2 = -77.4326676219507
x3 = -30.3087778181038
x4 = 54.5142238288206
x5 = 19.9567046393328
x6 = -64.8662970075916
x7 = -42.875148432463
x8 = 67.0805944431797
x9 = -24.0255925109243
x10 = 1.10714871779409
x11 = -5.1760365893855
x12 = -58.583111700412
x13 = -74.2910749683609
x14 = 48.231038521641
x15 = 73.3637797503593
x16 = -52.2999263932324
x17 = 13.6735193321533
x18 = 60.7974091360002
x19 = -49.1583337396426
x20 = 32.523075253692
x21 = -17.7424072037447
x22 = -14.6008145501549
x23 = 82.7885577111287
x24 = -20.8839998573345
x25 = -2.0344439357957
x26 = -11.4592218965651
x27 = 89.0717430183083
x28 = 76.5053724039491
x29 = 85.9301503647185
x30 = -86.8574455827201
x31 = -36.5919631252834
x32 = -68.0078896611814
x33 = -83.7158529291303
x34 = -71.1494823147711
x35 = 29.3814826001022
x36 = -55.4415190468222
x37 = 98.4965209790777
x38 = -33.4503704716936
x39 = -61.7247043540018
x40 = 63.93900178959
x41 = 4.24874137138388
x42 = 70.2221870967695
x43 = -8.31762924297529
x44 = -39.7335557788732
x45 = -96.2822235434895
x46 = -46.0167410860528
x47 = 92.2133356718981
x48 = 26.2398899465124
x49 = 57.6558164824104
x50 = 79.6469650575389
x51 = -99.4238161970793
x52 = 16.8151119857431
x53 = 10.5319266785635
x54 = 45.0894458680512
x55 = -27.167185164514
x56 = 95.3549283254879
x57 = -80.5742602755405
x58 = -93.1406308898997
x59 = -89.9990382363099
x60 = 38.8062605608716
x61 = 51.3726311752308
x62 = 7.39033402497368
x63 = 23.0982972929226
x64 = 41.9478532144614
x64 = 41.9478532144614