Question 1209768
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If a = sin50(1 + 2cos170°), 
b = sin170°(1 + 2cos140°), 
c = sin140°(1 + 2cos50°), 
then (3 - 2A)ˣ = (x + 1)², 
find x
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Regarding this problem,  I have two notices.


One notice is that quantity  A  is never defined in the posted problem.


@CPhill,  without any explanations,  uses    A = a + b + c,  by an arbitrary way.


May be,  it is correct,  but it deserves a separate mentioning.


Next, @CPhill reduces the problem to equation 


            {{{(sqrt(3))^x}}} = (x+1)^2.


He obtained  x = 0  as one of solutions.    It is correct.


But he missed another solution,  which does exist.   It is  x= -1.63775    (approximate).


It can be found graphically.    See the plot under this link

https://www.desmos.com/calculator/0s5w2nkiua


This plot is produced by free of charge online plotting tool  www.desmos.com/calculator


To get  x-coordinate of the intersection point,  click at this point.



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<U>Comment from student</U>: &nbsp;&nbsp;I made a mistake and I resent the complete question that &nbsp;&nbsp;A = a + b + c



<U>My response</U>: &nbsp;&nbsp;I expected to get from you something like 


&nbsp;&nbsp;&nbsp;&nbsp;"Thank you for your solution and for your teaching".



These are &nbsp;{{{highlight(highlight(FIRST))}}} &nbsp;{{{highlight(highlight(WORDS))}}} &nbsp;you should pronounce when you communicate with a  tutor.


Did your mother or father or other relatives taught you how to communicate with other people outside ?