Mathematics
Find the proper subsets of {x : x2 - 9x - 10 = 0}.
Sets
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Answer
x2 - 9x - 10 = 0
⇒ x2 - 10x + x - 10 = 0
⇒ x(x - 10) + 1(x - 10) = 0
⇒ (x - 10)( x + 1) = 0
⇒ (x - 10)= 0 or ( x + 1) = 0
⇒ x = 10 or x = -1
⇒ A = {10, -1}
If a set has n elements, the number of proper subsets = 2n - 1.
Here the set has 2 elements, the number of proper subsets = 22 - 1 = 2 x 2 - 1 = 3.
Proper subsets of A are ϕ, {10}, {-1}.
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