Question

the harmonic mean of a and b is 1/3 and harmonic mean of c and d 1/5 the harmonic mean of a,b,c,d is

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Harmonic mean of a and b is}\;\mathsf{\dfrac{1}{3}}$

$\textsf{Harmonic mean of c and d is}\;\mathsf{\dfrac{1}{5}}$

$\underline{\textbf{To find:}}$

$\textsf{Harmonic mean of a,b, c,d}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Harmonic mean:}}$

$\mathsf{Let\;x_1,x_2,x_3\;.\;.\;.\;.x_n\;be\;the\;given\;n\;values}$

$\mathsf{Then\;its\;Harmonic\;mean=\dfrac{n}{\dfrac{1}{x_1}+\dfrac{1}{x_2}+\;.\;.\;.+\dfrac{1}{x_n}}}$

$\textsf{Since harmonic mean of a and b is}\;\mathsf{\dfrac{1}{3},}$

$\mathsf{\dfrac{1}{3}=\dfrac{2}{\dfrac{1}{a}+\dfrac{1}{b}}}$

$\mathsf{\dfrac{1}{6}=\dfrac{1}{\dfrac{1}{a}+\dfrac{1}{b}}}$

$\implies\mathsf{\dfrac{1}{a}+\dfrac{1}{b}=6}$

$\textsf{Since harmonic mean of c and d is}\;\mathsf{\dfrac{1}{5},}$

$\mathsf{\dfrac{1}{5}=\dfrac{2}{\dfrac{1}{a}+\dfrac{1}{b}}}$

$\mathsf{\dfrac{1}{10}=\dfrac{1}{\dfrac{1}{c}+\dfrac{1}{d}}}$

$\implies\mathsf{\dfrac{1}{c}+\dfrac{1}{d}=10}$

$\underline{\mathsf{Harmonic\;mean\;of\;a,b,c,d:}}$

$\mathsf{=\dfrac{4}{\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}}}$

$\mathsf{=\dfrac{4}{6+10}}$

$\mathsf{=\dfrac{4}{16}}$

$\mathsf{=\dfrac{1}{4}}$

$\underline{\textbf{Answer:}}$

$\textsf{Harmonic mean of a,b,c,d is}\;\mathsf{\dfrac{1}{4}}$

$\underline{\textbf{Find more:}}$

Harmonic mean of the reciprocal of even numbers from 2 to 200 is

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Answer 2

Answer:

answer is = 1/4

Step-by-step explanation:

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