NTSE Stage 2 SAT 2014 Question Paper

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Question : 50 of 100

Marks: +1, -0

The number of integers

\n(<20)

for which

\n^2-3\n+3

is a perfect square is

0
1
2
3

Solution:

Let

\n^2-3\n+3=\k^2

⇒

\n^2-3\n+3-\k^2=0

For k to be an integer

(-3)^2-4(3-\k^2)

is a perfect square.
let

9-12+4x^2=\p^2

⇒

(2\k+\p)(2\k-\p)=3

⇒ k=1
Hence

n^2-3\n+2=0

⇒

\n=1,2

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