2012/013) solve √x+1 + √x-1 =1

(√x+1)^2 =(1 - √x-1)^2
so square both sides
x+1 = 1 - 2 √x-1 + x-1 = x - 2 √x-1

or 1 = - 2 √x-1

LHS is positive and RHS = -ve so contradiction thus no solution