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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
In a G.P., if the product of the first three terms is $ 27 $ and the set of all possible values for the sum of its first three terms is $ \mathbb{R} - (a, b) $, then $ a^2 + b^2 $ is equal to ______
Solution
Let first three terms of G.P. are $ \frac{A}{r},; A,; Ar $
$ \frac{A}{r} \cdot A \cdot Ar = 27 \Rightarrow A^3 = 27 \Rightarrow A = 3 $
$ 3\left( \frac{1}{r} + 1 + r \right) = 3 + 3\left( r + \frac{1}{r} \right) $
We know $ r + \frac{1}{r} \ge 2 $ or $ r + \frac{1}{r} \le -2 $
$ S \in \mathbb{R} - (-3, 9) $
$ a^2 + b^2 = 9 + 81 = 90 $
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