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

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

Grade:upto college level

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
(x-8)/(n-10)=n/x
=>x^2-8x-n(n-10)=0
For wq have no solution The dicriminant should be less than zero
so 64+4(1)n(n-10)<0
=>16+n^2-10n<0
=>(n-8)(n-2)<0
=>2<n<8
since n is a natural no so n=3,4,5,6,7
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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