2014/019 a+b+c+3=2(√a+√(b+1)+√(c-1)

find a^3 + b^3 + c^3

Solution
 

Let a = x^2, b = y^2−1, c = z^2+1
 

We get x^2+y^2+z^2+3=2x+2y+2z
Or(x^2–2x+1)+(y2–2y+1)+(z2−2z+1)=0
Or (x−1)^2+(y−1)^2+(z−1)^2=0
x = y = z = 1 or a = 1, b = 0, c = 2 

=> a^3+b^3+c^3 = 9