Question

x ²-1 <0 solve this quadratic in equalities​

Answer 1

$\large\underline{\sf{Solution-}}$

Given quadratic inequality is

$\rm :\longmapsto\: {x}^{2} - 1 < 0$

We know that

$\boxed{ \sf{ \: {x}^{2} - {y}^{2} = (x + y)(x - y)}}$

So, above expression can be reduced to

$\rm :\longmapsto\:(x + 1)(x - 1) < 0$

We know that,

If a and b are positive real numbers such that a < b then

$\boxed{ \sf{ \: (x - a)(x - b) < 0 \: \implies \: a < x < b}}$

So, using this

$\rm :\longmapsto\: - 1 < x < 1$

$\bf\implies \:x \: \in \: ( - 1, \: 1)$

Extra question :-

1. Solve the quadratic inequality :-

$\rm :\longmapsto\: {x}^{2} - 3x + 2 < 0$

$\rm :\longmapsto\: {x}^{2} - x - 2x+ 2 < 0$

$\rm :\longmapsto\:x(x - 1) - 2(x - 1) < 0$

$\rm :\longmapsto\:(x - 1)(x - 2) < 0$

$\rm :\longmapsto\:1 < x < 2$

$\bf\implies \:x \: \in \: ( 1, \: 2)$