Two harmonic means between $1 / 2, 4 / 17$ are

4 / 11, 2 / 7

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11 / 4, 7 / 2

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4 / 7, 2 / 11

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7 / 4, 11 / 2

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Solution

The correct option is B $4 / 11, 2 / 7$
Let the harmonic means be $H_{1}, H_{2}$
when the terms are reciprocaled, we get an arithmetic sequence with say $A_{1}, A_{2}$
so $2, A_{1}, A_{2}, \frac{17}{4}$ are in A.P
$A_{1} = 2 + d$
$A_{2} = 2 + 2 d$
so $2 + 3 d = \frac{17}{4}$
and then we get d= $\frac{3}{4}$
finding both arithmetic means and reciprocating them to find harmonic means..we get,
$H_{1} = \frac{4}{11}, H_{2} = \frac{2}{7}$

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Similar questions

$(i) \frac{3}{7} + \frac{- 4}{9} - \frac{- 11}{7} - \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} - \frac{1}{3} - \frac{2}{5} (i i i) \frac{4}{7} - \frac{- 8}{9} - \frac{- 13}{7} + \frac{17}{9}$

Q. Find the harmonic mean of the terms

\frac{4}{3}, \frac{4}{7}, \frac{4}{11}, \frac{4}{15}

Express the following in the form a + ib where a, b Є R.

Evaluate:

$3 (5 x - 7) - 2 (9 x - 11) = 4 (8 x - \frac{1}{3}) - 17$

Q. Find the roots of (P.S)

\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30} x \neq - 4, 7

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Two harmonic means between 1/2,4/17 are

Two harmonic means between $1 / 2, 4 / 17$ are