Question

The solution set of the equation [n]2 + [n + 1] – 3 = 0 (where [·] denotes greatest integer function) is


[–1, 0] ∪ [1, 2]


[–2, –1) ∪ [1, 2)


[1, 2]


(–3, –2) ∪ [2, 3)​

Answer 1

Given  : [n]² + [n + 1] – 3 = 0 (where [·] denotes greatest integer function) is

To Find : The solution set

[–1, 0] ∪ [1, 2]

[–2, –1) ∪ [1, 2)

[1, 2]

(–3, –2) ∪ [2, 3)​

Solution:

[n]² + [n + 1] – 3 = 0

[n] = x

=> [n + 1] = x + 1  

x² + x + 1 - 3 = 0

=> x²  + x - 2 = 0

=> x² + 2x - x - 2 = 0

=> x(x + 2) - 1(x + 2) = 0

=> (x - 1)(x + 2) = 0

=> x = 1  , x  = - 2

x = 1  => [n]  = 1

=> n =  [1, 2)

x  = - 2 => [n]  = -2

=> n =  [-2 , - 1)

n = [-2 , - 1)  ∪  [1, 2)  

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Answer 2

Answer:

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