SOLUTION: Let x-2,2√ 3, x-3 be the first 3 terms of a geometric sequence. Find the value of x (the quadratic equation can be solved by factoring).

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Question 986739: Let x-2,2√ 3, x-3 be the first 3 terms of a geometric sequence. Find the value of x (the quadratic equation can be solved by factoring).
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Since  ,   and    are the first  3  terms of a geometric sequence,  you have a proportion

=

(saying that the ratio of the second term to the first one is equal to the ratio of the third term to the second one).

From the proportion,

(x-2)*(x-3) = = 4*3 = 12.

Hence,

= ,

= ,

(x+1)*(x-6) = 0.

The roots are  -1  and  6.

Answer.  x = -1  or  x = 6.


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