The sum of the reciprocals of two successive positive integers is 33/272. Find the integers
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3
1/x + 1/(x+1) = 33/272
(x+1+x) /(x²+x) =33/272
544x +272 = 33x² + 33x
33x²-511x - 272 =0
(x+1+x) /(x²+x) =33/272
544x +272 = 33x² + 33x
33x²-511x - 272 =0
akash74:
now find the value of x
and the two integers will be x and x+1
Answered by
0
Let the integers be n & (n+1) ; then
(1/n) + 1/(n+1) = 33/272
(n+1+1)/(n^2+n = 33/272
(n+2)×272 = 33×(n^2+n)
272n + 544 = 33n^2 + 33n
33n^2-239n-544 = 0
(1/n) + 1/(n+1) = 33/272
(n+1+1)/(n^2+n = 33/272
(n+2)×272 = 33×(n^2+n)
272n + 544 = 33n^2 + 33n
33n^2-239n-544 = 0
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