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Find all n ? N, such that the equation x-8/n-10 = n/x has no solution x. Prob 3

Find all n ? N, such that the equation x-8/n-10 = n/x has no solution x.
Prob 3

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
9 years ago
We get :
x^2 - 8x + 10n - n^2 = 0
For no roots, D<0
64 - 4(10n-n^2) <0
64 - 40n + 4n^2 <0
n^2 - 10n + 16 < 0
(n-8)(n-2) < 0
n = (2,8)
Hence, n can be 3,4,5,6,7 for no solution of x
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty

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