√x+√x+1=√2x+1
Squaring both sides, we have
(√x+√x+1)2=(√2x+1)2
x+2√x(x+1)+x+1=2x+1
2x+1+2√x(x+1)−(2x+1)=0
(2√x(x+1))2=02implies4(x(x+1))=0
∴x(x+1)=0
x=0 or -1