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Grade:

                        

let [root(n 2 +1)]=[root(n 2 +λ)] , where n, λ€N . show that λ can have 2n different values.

11 years ago

Answers : (1)

mycroft holmes
272 Points
							

for 1≤ λ≤ 2n we have n2< n2+λ<(n+1)2

 

Hence n < √(n2+λ) < (n+1) and hence we have [√(n2+λ)] = [√(n2+1)] = n

 

If λ≤0 or λ>2n,  [√(n2+λ)] ≠ n

 

So these are the 2n values of λ for which the given equation holds

11 years ago
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