Question
Find the proper subsets of ${x : x^2 – 9x – 10 = 0}$
✓
Answer
$X^2 - 9x - 10 = 0$
$\Rightarrow x^2 - 10x + x - 10 = 0$
$\Rightarrow x(x-10)+1 (x-10) = 0$
$\Rightarrow (x-10)(x+1) = 0$
$\therefore$ Either $x-10 = 0$
$\Rightarrow x = 10$ or $x+1 = 0$
$\Rightarrow x = -1$
Given set $= \{-1, 10\}$
Proper subsets of this set $= φ, \{-1\}, \{10\}$
$\Rightarrow x^2 - 10x + x - 10 = 0$
$\Rightarrow x(x-10)+1 (x-10) = 0$
$\Rightarrow (x-10)(x+1) = 0$
$\therefore$ Either $x-10 = 0$
$\Rightarrow x = 10$ or $x+1 = 0$
$\Rightarrow x = -1$
Given set $= \{-1, 10\}$
Proper subsets of this set $= φ, \{-1\}, \{10\}$
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