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Cardinality of Sets

If A = x , x ...

Question

If $A = {x, x \in Z and | x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}}$ , then cardinality of set $A$ is

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Solution

$| x^{2} + 5 x - 6 | = 6 - 5 x - x^{2}$
Let $x^{2} + 5 x - 6 = t$ , then
$\Rightarrow | t | = - t \Rightarrow t \leq 0$
$\Rightarrow x^{2} + 5 x - 6 \leq 0$
$\Rightarrow (x + 6) (x - 1) \leq 0$
$\Rightarrow - 6 \leq x \leq 1$
$∴ x \in [- 6, 1]$
Since, $x \in Z$
$\Rightarrow x \in {- 6, - 5, - 4, - 3, - 2, - 1, 0, 1}$
$∴ n (A) = 8$

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Cardinality of Sets

Standard XII Mathematics

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