You do not need tosquare both sides, if ou dothe foowing substitution: Let t=sqrt(x), tthen we get: t+t^2=3/4 t^2+t-3/4=0 t=-1/2+-sqrt((1/2)^2-(-3/4)) t=-1/2+-sqrt(1/4+3/4) t=-1/2+-sqrt(1) t=-1/2+1=1/2 or t=-1/2-1=-3/2 Recall t=sqrt(x), and thinof definition of square root of x as the non negative soution of t^2=x: We reject t=-3/2, since it is ower than 0. So t=1/2 and x=t^2=(1/2)^2=1/4 With squaring the equation, you have the risk to get additiona (errornous) soutions.
