If the sum of two number is10 .if sum of their reciprocal 5/12.find the sum
Answers
let the two integer be M and N , it is given that the sum of the two integer is 10 . this gives the equation
M+N = 10 ............. ............... (1)
it is also given that the sum of their reciprocal is 5 by 12 the reciprocal of M is 1/m and the reciprocal of an is
1/n therefore we get the second equation
1/m + 1/n = 5/12
or, (m+n)/mn=5/12
substituting for m+n =10 from (1),
10/mn = 5/12
divide both side by 5 to get
2/ mn = 1/12
taking reciprocal on both side
mn/2 = 12
cross multiplying
mn = 24
this gives m = 24/ n
substituting this value of m in (1)
24 / n+n = 10
taking LCM
(24+n^2)/n= 10
cross multiplying
24 + n^2 = 10 n
or, n ^ 2 - 10n + 24 = 0
factorising
n^2 - 6n - 4n + 24= 0
or, n(n-6) -4(n-6)= 0
or, (n-6) (n-4)= 0
this gives two solution for n: 6 and 4
the corresponding solution for m are obtained from (1)
as 10-n and they are
4 and 6
Thus there are two pairs of solution for (m,n),
(4,6) and (6,4)
it follows from above that
the largest integer is 6
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