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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:12

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
(x-8)/(n-10)=n/x
=>x(x-8)=n(n-10)
=>x^2-8x-n(n-10)=0
For Eq has no solution in x, B^2-4AC<0
=>64+4(1)(n)(n-10)<0
=>16+n(n-10)<0
=>n^2-10n+16<0
=>(n-8)(n-2)<0
=> 2 <n<8
So n=3,4,5,6,7

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
kaushik bhargav
20 Points
6 years ago
(x-8)/(n-10)=n/x
=>x(x-8)=n(n-10)
=>x^2-8x-n(n-10)=0
For Eq has no solution in x, B^2-4AC
=>64+4(1)(n)(n-10)
=>16+n(n-10)
=>n^2-10n+16
=>(n-8)(n-2)
=> 2
So n=3,4,5,6,7

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