Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesH.P.Medium2 minQB

MathematicsMediumsingle choice

If $a, b, c$ are distinct positive reals in H.P., then the value of the expression $\frac{b + a}{b - a} + \frac{b + c}{b - c}$ is equal to

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Answer:

Solution:

$b = \frac{2 a c}{a + c}$ . Then $\frac{b}{a} = \frac{2 c}{a + c}$ , so $\frac{b + a}{b - a} = \frac{2 c + ( a + c )}{2 c - ( a + c )} = \frac{3 c + a}{c - a} \dots (1)$ Similarly $\frac{b}{c} = \frac{2 a}{a + c}$ , so $\frac{b + c}{b - c} = \frac{3 a + c}{a - c} \dots (2)$ (1)+(2): $\frac{3 c + a - 3 a - c}{c - a} = \frac{2 c - 2 a}{c - a} = 2$ .

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

⏱ 2mℹ️ Source: QB

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