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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:11

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago
(x-8)x=n(n-10)
x^2-8x-n(n-10)
for no real solution b^2-4ac<0

64-4n(n-10)<0
64-4n^2+40n<0
-4n^2+40n+64<0
n^2-10n-16>0
n^2-10n+25-25-16
(n-5)^2-41>0
for n-5>7,(n-5)^2-41>0
imply n>12

sher mohammad
b.tech, iit delhi




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