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Empty Set

Write which s...

Question

Write which singleton set does the following represent?
$x = {x : x \in x^{2} - 3 x + 2 = 0 : x > 1}$

{1}

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{2}

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{- 2}

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{- 1}

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Solution

The correct option is D ${2}$
$x = {x : x \in x^{2} - 3 x + 2 = 0 : x > 1}$
Let's solve the equation $x^{2} - 3 x + 2 = 0$
$x^{2} - 3 x + 2 = 0$
$\Rightarrow x^{2} - 2 x - x + 2 = 0$
$\Rightarrow x (x - 2) - (x - 2) = 0$
$\Rightarrow (x - 1) (x - 2) = 0$
$x = 1$ or $x = 2$
But we have to choose value of $x$ which is greater then $1$ i.e. $2.$
Hence, $x = {x : x \in x^{2} - 3 x + 2 = 0 : x > 1} = {2}$

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