2014/032) How many real solutions does the following system have. a+ b = 2 ab –c^2 = 1

Let a = 1 – x and b = 1 + x

So ab – c^2 = (1-x)(1+x) – c^2 = 1 – x^2- c^2 = 1

Or x^2 + c^2 = 0 => x = c = 0

So c = 0 and a=b = 1,

So one solution a =1, b= 1, c = 0