Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=sqrt(3)/2
-
Equation 5-2*(x-1)=4-x
-
Equation (x-2)^2=(x-9)^2
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Equation x^2-3x=0
- Express {x} in terms of y where:
- -6*x+1*y=14
- 18*x+14*y=-11
- -6*x-20*y=8
- 20*x-4*y=-7
- Derivative of:
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ctgx/2
- Integral of d{x}:
- ctgx/2
- √3
- Sum of series:
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√3
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Identical expressions
- ctgx/ two =√ three
- ctgx divide by 2 equally √3
- ctgx divide by two equally √ three
- ctgx divide by 2=√3
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Similar expressions
- 2*(a/x+arctg(x/2))=0
- 3ctg(x/2-п/4)-√3=0
ctgx/2=√3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cot{\left(x \right)}}{2} = \sqrt{3}$$
transform
$$\frac{\cot{\left(x \right)}}{2} - \sqrt{3} - 1 = 0$$
$$\frac{\cot{\left(x \right)}}{2} - \sqrt{3} - 1 = 0$$
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:
$$\frac{w}{2} - \sqrt{3} = 1$$
Divide both parts of the equation by (w/2 - sqrt(3))/w
We get the answer: w = 2 + 2*sqrt(3)
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\frac{\cot{\left(x \right)}}{2} = \sqrt{3}$$
transform
$$\frac{\cot{\left(x \right)}}{2} - \sqrt{3} - 1 = 0$$
$$\frac{\cot{\left(x \right)}}{2} - \sqrt{3} - 1 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Expand brackets in the left part
-1 + w/2 - sqrt3 = 0
Move free summands (without w)
from left part to right part, we given:
$$\frac{w}{2} - \sqrt{3} = 1$$
Divide both parts of the equation by (w/2 - sqrt(3))/w
w = 1 / ((w/2 - sqrt(3))/w)
We get the answer: w = 2 + 2*sqrt(3)
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
Rapid solution
[src]
/ ___\ x1 = acot\2*\/ 3 /
$$x_{1} = \operatorname{acot}{\left(2 \sqrt{3} \right)}$$
x1 = acot(2*sqrt(3))
Sum and product of roots
[src]
sum
/ ___\ acot\2*\/ 3 /
$$\operatorname{acot}{\left(2 \sqrt{3} \right)}$$
=
/ ___\ acot\2*\/ 3 /
$$\operatorname{acot}{\left(2 \sqrt{3} \right)}$$
product
/ ___\ acot\2*\/ 3 /
$$\operatorname{acot}{\left(2 \sqrt{3} \right)}$$
=
/ ___\ acot\2*\/ 3 /
$$\operatorname{acot}{\left(2 \sqrt{3} \right)}$$
acot(2*sqrt(3))
Numerical answer
[src]
x1 = -49.9844475559339
x2 = -27.9932989808053
x3 = 59.9712953197089
x4 = -153.657005124397
x5 = -31.1348916343951
x6 = 9.70581286227219
x7 = 100.811999816376
x8 = 37.9801467445803
x9 = -34.2764842879849
x10 = -43.7012622487543
x11 = -2022.90463401032
x12 = -6.00215040567677
x13 = 44.2633320517599
x14 = 3.42262755509261
x15 = 15.9889981694518
x16 = -65.6924108238828
x17 = -93.966744706191
x18 = -71.9755961310624
x19 = 66.2544806268885
x20 = 81.9624438948374
x21 = -78.258781438242
x22 = 22.2721834766314
x23 = 75.6792585876579
x24 = -21.7101136736257
x25 = -12.2853357128564
x26 = -87.6835593990114
x27 = 88.245629202017
x27 = 88.245629202017