1.Let ABC be a triangle. Let B' and C' denote respectively the reflection of B and C in the internal angle bisector of angle A. Show that the triangles ABC and AB'C' have the same incentre.

2.Let P(x)=x*x+ax+b be a quadratic polynomial with real coefficients. suppose there are real numbers s is not equal to t such that P(s)=t and P(t)=s.

Prove that b-st is a root of the equation x*x+ax+b-st=0

3.Find all integers a,b,c such that    a*a=bc+1,b*b=ca+1