weird equation (for me)

[Kochu]

the problem states:

what i tried is

 

[HallsofIvy]

Yes \(\displaystyle a^2+ 2a+ 1= (a+ 1)^2\) and \(\displaystyle a^2- 4a+ 4= (a- 2)^2\).

If -1< a< 2 then -2< a- 1<1 so \(\displaystyle 1< (a- 1)^2< 4\) and -3< a- 2< 0 so \(\displaystyle 0< (a- 2)^2< 4\).
I don't see how that can come out to a single number!

 

[pka]

the problem states: View attachment 19190

what i tried is View attachment 19193

If \(y-\sqrt{x^2}\) then \(y=|x|\).
\(\sqrt{a^2+2a+1}=\sqrt{(a+1)^2}=|a+1|\) AND \(\sqrt{a^2-4a+4}=\sqrt{(x-2)^2}=|a-2|\)
LOOK HERE

 

[Kochu]

ahhhhhhhhhhhhhh i see, so i have to use the definition of abs value, using the domain it ends a+1 + -a+2 it cancels and the answer is 3 !! many thanks hallsoflvy and pka : )