anonymous
  • anonymous
solve cotX^2+4cotX-7=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
find the general solution
anonymous
  • anonymous
@Michele_Laino
SolomonZelman
  • SolomonZelman
you can at first say, let \(\cot(x)=a\), which will give you the following quadratic equation, \(a^2+4a-7=0\)

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SolomonZelman
  • SolomonZelman
Solve this equation for a, and after you find the solutions for a, you can find the value of x, using the fact that \(a=\cot(x)\)
SolomonZelman
  • SolomonZelman
(well, not the value of x, but a set of solutions, but I hope you see what I mean)
anonymous
  • anonymous
what about the general solution?
mathstudent55
  • mathstudent55
When you write \(\cot x^2\), do you really mean \(\cot^2 x\) ?
anonymous
  • anonymous
the latter
SolomonZelman
  • SolomonZelman
yes, mathstudent55 I would assume so:) I didn't even notice that mistake (if it is a mistake)
SolomonZelman
  • SolomonZelman
have you solved for "a" (using a substitution of a=cot(x) that I offered) ?
anonymous
  • anonymous
yes but that just gave me -2 +or-sqrt(44)
SolomonZelman
  • SolomonZelman
i got mixed up for some reason
SolomonZelman
  • SolomonZelman
a²-4a-7=0 a²-4a=7 a²-4a+4=7+4 a²-4a+4=11 (a-2)²=11 a-2=±√11 a=-2±√11 that is what I get
anonymous
  • anonymous
its +4a
SolomonZelman
  • SolomonZelman
oh, tnx for catching me
anonymous
  • anonymous
(y)
SolomonZelman
  • SolomonZelman
oh, my fault, i did the step incorrectly
SolomonZelman
  • SolomonZelman
a²-4a-7=0 a²-4a=7 a²-4a+4=7+4 a²-4a+4=11 (a-2)²=11 a-2=±√11 a=2±√11 that is what I get if -4a ------------------ thus with +4a i would get now with +4a i get a²+4a-7=0 a²+4a=7 a²+4a+4=7+4 a²+4a+4=11 (a+2)²=11 a+2=±√11 a=-2±√11
SolomonZelman
  • SolomonZelman
and by the quadratic formula a²+4a-7=0 \(\large\color{black}{ \displaystyle \frac{-4\pm\sqrt{(4)^2-4(-7)(1)} }{2} }\) \(\large\color{black}{ \displaystyle \frac{-4\pm\sqrt{44} }{2} }\) \(\large\color{black}{ \displaystyle \frac{-4}{2}\pm\frac{\sqrt{44} }{2} }\)
SolomonZelman
  • SolomonZelman
see I am getting the same thing a = -2±√11
anonymous
  • anonymous
okay, yay thanks, i get it now!
SolomonZelman
  • SolomonZelman
yes, so \(\cot(x)=-2+\sqrt{11}\) or \(\cot(x)=-2-\sqrt{11}\)
SolomonZelman
  • SolomonZelman
\(\cot^{-1}(-2+\sqrt{11})=a\) or \(\cot^{-1}(-2-\sqrt{11})=a\)

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