1. The problem statement, all variables and given/known data For U(w)=sqrt(w), prove that U(pie(x)+(1-pie)y) > pie*U(x)+(1-pie)U(y) 2. Relevant equations sqrt(x)=x^(1/2) 3. The attempt at a solution I have: sqrt(pie(x)+(1-pie)y) > pie*sqrt(x)+(1-pie)sqrt(y) so... (pie(x)+(1-pie)y)^(1/2) > pie*(x)^1/2+(1-pie)(y)^1/2 From here I don't know where to go. I don't have much experience with proofs so can anyone give some guidance? Thanks for your help!