Question

the sum of 3 members are in HP. is 37 and the sum of their reciprocals is 1/4.. find the numbers...


ans-15,12,10 etc.... or 10,12,15

Answer 1

hello...



please refer the above attachment....


thank you...


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Answer 2

Answer:15,12,10

Step-by-step explanation:

let a-d, a, a+d are in A.P. so 1/a-d, 1/a, 1/a+d are in H.P.

as given

a-d+a+a+d =1/4

3a = 1/4

a= 1/12

again

$\frac{1}{a-d}+\frac{1}{a}+\frac{1}{a+d}=37\\\\\frac{12}{1-12d}+12+\frac{12}{1+12d}=37\\\\\frac{1}{1-12d}+\frac{1}{1+12d}=\frac{25}{12}\\\\\frac{1+12d+1-12d}{1-144d^{2}}=\frac{25}{12}\\\\d=\frac{1}{60}$

so numbers are 1/a-d, 1/a, 1/a+d or 15,12,10