Question

How do you solve `z^2-6z+7<2`?

Answer 1

The answer is `z in ] 1,5 [`

Explanation:

Let's rearrange the inequation

`z^2-6z+7<2`

`z^2-6z+5<0`

Let's factorise

`(z-5)(z-1)<0`

Let `f(z)=(z-5)(z-1)`

Now. we can do the sign chart

`color(white)(aaaa)` `z` `color(white)(aaaaa)` `-oo` `color(white)(aaaa)` `1` `color(white)(aaaaaa)` `5` `color(white)(aaaaaa)` `+oo`

`color(white)(aaaa)` `z-1` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `z-5` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

`color(white)(aaaa)` `f(z)` `color(white)(aaaaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

Therefore,

`f(z)<0`, when `z in ] 1,5 [`