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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Medium2 minQB

MathematicsMediumsingle choice

If $a^{2} + b^{2}, ab + b c$ and $b^{2} + c^{2}$ are in G.P. then $a, b, c$ are in

Options:

Answer:

Solution:

$(ab + b c)^{2} = (a^{2} + b^{2}) (b^{2} + c^{2})$ $\Rightarrow a^{2} b^{2} + b^{2} c^{2} + 2 a b^{2} c = a^{2} b^{2} + a^{2} c^{2} + b^{4} + b^{2} c^{2} \Rightarrow (b^{2} - a c)^{2} = 0 \Rightarrow b^{2} = a c \Rightarrow a, b, c are in G.P. \Rightarrow Option (B)$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

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