Question

if |x-2|<1, prove that |x^2+2x+2|<17

Answer 1

x+4
--------------------
x-2 | x^2 +2x +2
-(x^2-2x)
--------------
4x+2
-(4x-8)
--------
10

\[|(x-2)(x+4)+10|=|(x-2)(x-2+6)+10|=|(x-2)(x-2)+6(x-2)+10|\]
\[=|(x-2)^2+6(x-2)+10|<|(x-2)^2|+|6(x-2)|+|10|<1^2+6(1)+10\]

Answer 2

Thanks, that's an awesome answer. I tried polynomial division, but I didn't know what to do with it lol

Answer 3

thanks :)

Answer 4

and your welcome