Find the values of u for the inequality u2 -2u + 1

We have to solve the inequality u^2 -2u + 1 <
16.

u^2 -2u + 1 <
16

=> u^2 - 2u - 15 <
0

=> u^2 - 5u + 3u - 15 <
0

=> u( u - 5) + 3( u -5) <
0

=> (u +3) (u - 5)<
0

Now for this to be true either of the terms u + 3 and u-5
should be negative.

=> u+3> 0 and u-5
< 0

=> u > -3 and u <
5

This gives us that u lies in (-3 ,
5)

u+3 < 0 and u - 5>
0

=> u < -3 and u > 5 which is not
possible.

So the only valid value of u lie in
( -3, 5)