Question 101464
sqrt(x+1)+sqrt(2x)=1
(sqrt(2x)-1)^2=(-sqrt(x+1))^2
2x-2sqrt(2x)+1=x+1
x=2sqrt(2x)
x^2=4*2x square both sides
x^2=8x
x^2-8x=0
x(x-8)=0 factor
x=0, x=8
Check:
sqrt(0+1)+sqrt(2*0)=1 true
sqrt(8+1)+sqrt(2*8)=1 false
.
x=0 is the only answer.
Ed