Question 1208200
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<pre>

If 1st term of a GP is x and 3rd term is y, then

    y = {{{x*r^2}}},    (1)


where r is the common ratio.  If x is not zero, then we can divide both sides of this equation by x

    {{{r^2}}} = {{{y/x}}}.    (2)


Notice that in this case, when x =/= 0,  from formula (1),  both  y and x have the same sign
(both are either positive or negative), so the ratio  {{{y/x}}}  is non-negative.


Hence,  we can take square root of  {{{y/x}}}

    r = +/- {{{sqrt(y/x)}}},


and in the case x =/= 0  it is the final answer to the problem's question, 
giving two possible values for r, if y =/= 0, or single zero, of y=0.



In the special case  x=0  we CAN NOT divide by x (by zero), so formula (2) does not work.


In this case, the geometric progression is degenerated: all its terms are zeros.


So, the complete answer is  r = +/- {{{sqrt(y/x)}}},  if x =/= 0  (two possible values, if y =/= 0; or single 0, if y=0)
                                
                            or any real number, if x = 0, but the GP in this case is degenerated and consists of zeros.
</pre>

Solved completely with giving a complete answer.


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This problem is, obviously, a trap.

The trap is that a COMPLETE answer is required, including the case x=0.