Solve the following inequalities and write the solution set using… - Vidyadip

Question

Solve the following inequalities and write the solution set using interval notation.$x^2-x>20$

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Answer

$x^2-x>20$
$\therefore x^2-x-20>0$
$\therefore x^2-5 x+4 x-20>0$
$\therefore(x-5)(x+4)>0$
$\therefore \text { either } x-5>0 \text { and } x+4>0 \text { or } x-5<0 \text { and } x+4<0$
Case I: $x – 5 > 0$ and $x + 4 > 0 \therefore x > 5$ and $x > -4 \therefore x > 5$ ….(i)
Case II: $x – 5 < 0$ and $x + 4 < 0 \therefore x < 5$ and $x < -4 \therefore x < -4$ …..(ii)
From (i) and (ii), we get $x \in (-\propto, – 4) \cup (5, \propto)$

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