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- Equation:
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Equation 9(x-1)=x+15
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Equation sin(x/3)=1/2
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Equation 3*x=8
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Equation x^2-8x+12=0
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Identical expressions
- √ three ctg(x+pi)-3= zero
- √3ctg(x plus Pi ) minus 3 equally 0
- √ three ctg(x plus Pi ) minus 3 equally zero
- √3ctgx+pi-3=0
- √3ctg(x+pi)-3=O
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Similar expressions
- √3ctg(x-pi)-3=0
- √3ctg(x+pi)+3=0
√3ctg(x+pi)-3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
_______________ \/ 3*cot(x + pi) - 3 = 0
$$\sqrt{3 \cot{\left(x + \pi \right)}} - 3 = 0$$
Detail solution
Given the equation
$$\sqrt{3 \cot{\left(x + \pi \right)}} - 3 = 0$$
transform
$$\sqrt{3} \sqrt{\cot{\left(x \right)}} - 3 = 0$$
$$\sqrt{3 \cot{\left(x + \pi \right)}} - 3 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Given the equation
$$\sqrt{3} \sqrt{\cot{\left(x \right)}} - 3 = 0$$
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:
$$\left(\sqrt{3}\right)^{2} \left(\sqrt{0 w + \cot{\left(x \right)}}\right)^{2} = 3^{2}$$
or
$$3 \cot{\left(x \right)} = 9$$
Expand brackets in the left part
This equation has no roots
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\sqrt{3 \cot{\left(x + \pi \right)}} - 3 = 0$$
transform
$$\sqrt{3} \sqrt{\cot{\left(x \right)}} - 3 = 0$$
$$\sqrt{3 \cot{\left(x + \pi \right)}} - 3 = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Given the equation
$$\sqrt{3} \sqrt{\cot{\left(x \right)}} - 3 = 0$$
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:
$$\left(\sqrt{3}\right)^{2} \left(\sqrt{0 w + \cot{\left(x \right)}}\right)^{2} = 3^{2}$$
or
$$3 \cot{\left(x \right)} = 9$$
Expand brackets in the left part
3*cotx = 9
This equation has no roots
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 = -65.651695170989
x3 = 66.2951962797823
x4 = 22.3128991295252
x5 = -21.6693980207319
x6 = 75.7199742405517
x7 = -5.96143475278294
x8 = -71.9348804781686
x9 = 85.1447522013211
x10 = -68.7932878245788
x11 = -46.8021392494503
x12 = 44.3040477046537
x13 = 31.7376770902946
x14 = 19.1713064759354
x15 = -24.8109906743217
x16 = 53.7288256654231
x17 = 38.0208623974742
x18 = -87.6428437461176
x19 = 16.0297138223456
x20 = 60.0120109726027
x21 = -56.2269172102196
x22 = -90.7844363997074
x23 = 88.2863448549109
x24 = 41.162455051064
x25 = 82.0031595477313
x26 = -43.6605465958605
x27 = -93.9260290532972
x28 = -49.9437319030401
x29 = 63.1536036261925
x30 = -78.2180657853482
x31 = -34.2357686350911
x32 = -2.81984209919315
x33 = 97.7111228156802
x34 = -100.209214360477
x35 = 9.74652851516602
x36 = -12.2446200599625
x36 = -12.2446200599625