Question

The set A = {x : x4 – x3 – x2 = 0 and x ∈ N} represents

Answer 1

Given :  set A = {x : x⁴ – x³ – x² = 0 and x ∈ N}

To find : Set A  

Solution:

set A = {x : x⁴ – x³ – x² = 0 and x ∈ N}

x⁴ – x³ – x² = 0

=> x²(x²  - x - 1) = 0

=> x² = 0   or x²  - x - 1 = 0

=> x = 0       or  x  =  (1 ± √5)/2

but x ∈ N  N = { 1 , 2 , 3 , 4 ......}

Hence no value of x  belongs to N

so A = { }  = null set = Empty set = Ф

Set A is  null set = Empty set = Ф

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