Consider three distinct real numbers \( a, b, c \) in a G.P. with \... VIDEO
Consider three distinct real numbers \( a, b, c \) in a G.P. with \( a^{2}+b^{2} \) \( +c^{2}=t^{2} \) and \( a+b+c=\alpha \). The sum of the common ratio and its
P reciprocal is denoted by \( S \).
W.
If \( a, b \), and \( c \) also represent the sides of a triangle, then the complete set of \( \alpha^{2} \) is
(1) \( \left(\frac{1}{3}, 3\right) \)
(2) \( (2,3) \)
(3) \( \left[\frac{1}{3}, 2\right] \)
(4) \( \left(\frac{\sqrt{5}+3}{2}, 3\right) \)
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