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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

If $lo g (a + c), lo g (a + b), lo g (b + c)$ are in A.P. and $a, c, b$ are in H.P., with $a, b, c > 0$ , find $a + b$ .

Options:

Answer:

Solution:

Let $t = a + b$ . The logarithmic condition gives $(a + c) (b + c) = t^{2}$ , while H.P. gives $2 ab = c t$ . Substitution yields $t^{2} = c t /2 + c t + c^{2}$ , or $2 t^{2} - 3 c t - 2 c^{2} = 0$ . As $t, c > 0, t = 2 c$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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