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Question
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
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Solution
Let the terms of the the given G.P. be
Similarly, sum of the G.P. = 65
\[\frac{15}{r} + 15 + 15r = 65\]
\[ \Rightarrow 15 r^2 + 15r + 15 = 65r\]
\[ \Rightarrow 15 r^2 - 50r + 15 = 0\]
\[ \Rightarrow 5\left( 3 r^2 - 10r + 3 \right) = 0\]
\[ \Rightarrow 3 r^2 - 10r + 3 = 0\]
\[ \Rightarrow \left( 3r - 1 \right)\left( r - 3 \right) = 0\]
\[ \Rightarrow r = \frac{1}{3}, 3\]
Hence, the G.P. for a = 15 and r = \[\frac{1}{3}\] is 45, 15, 5.
And, the G.P. for a = 15 and r = 3 is 5, 15, 45.
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