sqrt(a^2 + a + 1) = 2 - |a|

sqrt(a^2 + a + 1) = 2 - |a|

First how about you get rid of the square root which also helps you get rid of the absolute sign on the right side.

a^2 + a + 1 = (2-|a|)^2 = 4 - 4a + a^2

This should simplify matters greatly. Try it and report back how things work out.

I like the approach, rpray, but note that the RHS squares to

4 - 4|a| + a^2

... then you can solve by the two cases for a. Otherwise, you lose one of the solutions.

Arcsine - you got me there! I stand corrected.

Thank you, rpray2007 and ArcSine! I tried something similar too, but I got struck at the modulus. Now I know what I have to do :)